Main Thesis Report

PROBABILISTIC CALCULATION FOR FATIGUE LIFE OF THE STEEL CATENARY RISER A THESIS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

SUBMITTED TO THE DEPARTMENT OF NAVAL ARCHITECTURE & MARINE ENGINEERING OF STRATHCLYDE UNIVERSITY

BY RONGRITH PICHAIYONGWONGDEE AUGUST 2011

This thesis is the result of the author's original research. It has been composed by the author and has not been previously submitted for examination which has led to the award of a degree. The copyright of this thesis belongs to the author under the terms of the United Kingdom Copyright Acts as qualified by University of Strathclyde Regulation 3.50. Due acknowledgement must always be made of the use of any material contained in, or derived from, this thesis. Signed:

Date:

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To Mom and Dad

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Abstract In the past decade, the free-hanging SCR is an alternative riser system since the oil reservoirs are found at the depth greater than 1,000 meters where the flexible riser application is limited by the extreme hydrostatic pressure. In this circumstance, the SCR can overcome the difficulty by adding extra pipe thickness. Also, extra benefits of this SCR riser system are inexpensive, simpler installation and easier maintenance which allow companies operate the deepwater field with less complexity system. However, the failure of riser can be occurred and its possibility is greatly associated with the random nature of environmental loads e.g. waves, winds and currents because these environmental loads have immense influence on the vessel’s motions. Therefore, evaluating these factors is an essential criterion in the riser design to estimate the fatigue life. In the past, the riser design was based on the deterministic calculations which the loads are based on common sea states. It was merely possible to utilize all wave and wind data in the calculations because the calculations were limited by its complexity, requirement for huge data storage and long simulation time. However, with the improved capability of today computer, the detail engineering simulation can be done to present accurate and meaningful answers. In this study, the optimal design of the steel catenary riser (SCR) will be examined, even though; the riser fatigue life will be calculated by using probabilistic approach.

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List of Figures Figure 1 World map of the deepwater oil exploration and production. ....................... 4  Figure 2 Segments and nodes in riser model. ............................................................ 19  Figure 3 Wall tension and pipe pressure force. .......................................................... 19  Figure 4 Frame of reference of pipe stress calculation. ............................................. 20  Figure 5 Free-body diagrams for FPSO and riser system. ......................................... 22  Figure 6 Wave force RAOs for surge and heave motions ......................................... 23  Figure 7 Estimate riser profile in static condition. ..................................................... 25  Figure 8 Nodes displacement in X-axis. .................................................................... 27  Figure 9 Nodes displacement in Y-axis. .................................................................... 27  Figure 10 Tensile stress profiles for each riser segment. ........................................... 29  Figure 11 SN curve (API Class X)............................................................................. 36  Figure 12 Block diagram represents the approach for project (1). ............................ 37  Figure 13 Block diagram represents the approach for project (2). ............................ 38  Figure 14 Block diagram represents the approach for project (3). ............................ 38  Figure 15 Location of Montara field, Timor Sea. ...................................................... 40  Figure 16 Deep water areas in the Timor Sea (water depth > 500 Meters). .............. 40  Figure 17: Existing development fields in the Timor Sea.......................................... 41  Figure 18 Swells from south Indian Ocean to Timor Sea. ......................................... 43  Figure 19 Annual wave rose diagrams measured at Jabiru field. .............................. 44  Figure 20 Monthly wave rose diagrams measured in Jabiru field. ............................ 45  Figure 21 Montara FPSO. .......................................................................................... 47  Figure 22 Montara FPSO specifications. ................................................................... 48  Figure 23 FPSO model (Side view). .......................................................................... 49  Figure 24 FPSO model (Front view).......................................................................... 49  Figure 25 Plot of maximum von Mises stress and allowable pipe stress. .................. 51  Figure 26 Plot of riser utilization (API RP 2RD)....................................................... 51  Figure 27 Bending radius profile. .............................................................................. 53  Figure 28 Riser curvature profile. .............................................................................. 53  Figure 29 Pipe collapse pressure and the net hydrostatic pressure. ........................... 55 

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Figure 30 Shape configurations of the steel catenary riser. ....................................... 57  Figure 31 Mean von Mises combined stress (vary outside diameter). ....................... 58  Figure 32 Mean axial stress profile (vary outside diameter)...................................... 59  Figure 33 Mean bending stress profile (vary outside diameter). ............................... 59  Figure 34 Mean hoop stress profile (vary outside diameter). .................................... 60  Figure 35 Riser shapes for various length of riser. .................................................... 61  Figure 36 Mean von Mises stress profiles (vary length of riser). .............................. 62  Figure 37 Mean axial stress profiles (vary length of riser). ....................................... 62  Figure 38 Mean bending stress profiles (vary length of riser). .................................. 63  Figure 39 Mean hoop stress profiles (vary length of riser). ....................................... 63  Figure 40 Riser shape configurations when vary the initial offset of FPSO.............. 64  Figure 41 Mean von Mises combined stress (vary initial offset). .............................. 65  Figure 42 Mean axial stress profile (vary initial offset)............................................. 66  Figure 43 Mean bending stress profile (vary initial offset). ...................................... 66  Figure 44 Mean hoop stress profile (vary initial offset). ........................................... 67  Figure 45 FPSO heave motion (vary FPSO size). ..................................................... 68  Figure 46 Mean von Mises combined stress (vary FPSO size). ................................ 69  Figure 47 Mean axial stress profile (vary FPSO size). .............................................. 69  Figure 48 Mean bending stress profile (vary FPSO size). ......................................... 70  Figure 49 Mean hoop stress profile (vary FPSO size). .............................................. 70  Figure 50 Wave scatter diagrams prepared in 4 directions. ....................................... 76  Figure 51 Cumulative probability distribution of maximum stress. .......................... 78  Figure 52 Cumulative probability distribution of stress range................................... 79  Figure 53 Cumulative probability distribution of the fatigue life. ............................. 80  Figure 54 Probability distribution of the fatigue life. ................................................ 80  Figure 55 Displacement RAOs (Amplitude, 0 degree wave direction) ..................... 85  Figure 56 Displacement RAOs (Phase, 0 degree wave direction) ............................. 85  Figure 57 Displacement RAOs (Amplitude, 30 degree wave direction) ................... 86  Figure 58 Displacement RAOs (Phase, 30 degree wave direction) ........................... 86  Figure 59 Displacement RAOs (Amplitude, 60 degree wave direction) ................... 87  Figure 60 Displacement RAOs (Phase, 60 degree wave direction) ........................... 87  Figure 61 Displacement RAOs (Amplitude, 90 degree wave direction) ................... 88 

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Figure 62 Displacement RAOs (Phase, 90 degree wave direction) ........................... 88  Figure 63 Displacement RAOs (Amplitude, 120 degree wave direction) ................. 89  Figure 64 Displacement RAOs (Phase, 120 degree wave direction) ......................... 89  Figure 65 Displacement RAOs (Amplitude, 150 degree wave direction) ................. 90  Figure 66 Displacement RAOs (Phase, 150 degree wave direction) ......................... 90  Figure 67 Displacement RAOs (Amplitude, 180 degree wave direction) ................. 91  Figure 68 Displacement RAOs (Phase, 180 degree wave direction) ......................... 91  Figure 69 Wave load RAOs (Operating draft, 0 degree wave direction)................... 96  Figure 70 Wave load RAOs (Phase, 0 degree wave direction) .................................. 96  Figure 71 Wave load RAOs (Operating draft, 30 degree wave direction)................. 97  Figure 72 Wave load RAOs (Phase, 30 degree wave direction) ................................ 97  Figure 73 Wave load RAOs (Operating draft, 60 degree wave direction)................. 98  Figure 74 Wave load RAOs (Phase, 60 degree wave direction) ................................ 98  Figure 75 Wave load RAOs (Operating draft, 90 degree wave direction)................. 99  Figure 76 Wave load RAOs (Phase, 90 degree wave direction) ................................ 99  Figure 77 Wave load RAOs (Operating draft, 120 degree wave direction)............. 100  Figure 78 Wave load RAOs (Phase, 120 degree wave direction) ............................ 100  Figure 79 Wave load RAOs (Operating draft, 150 degree wave direction)............. 101  Figure 80 Wave load RAOs (Phase, 150 degree wave direction) ............................ 101  Figure 81 Wave load RAOs (Operating draft, 180 degree wave direction)............. 102  Figure 82 Wave load RAOs (Phase, 180 degree wave direction) ............................ 102 

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List of Tables Table 1: Stress definition according to API 2RD....................................................... 30  Table 2 Design matrix for rigid risers ........................................................................ 32  Table 3 S-N curve parameter for API Class-X .......................................................... 35  Table 4 Pipeline specifications .................................................................................. 50  Table 5 Simulation parameters used in the base case ................................................ 56  Table 6 Fatigue damage sensitivity (vary outside diameter) ..................................... 58  Table 7 Cases for riser length sensitivity analysis ..................................................... 61  Table 8 Fatigue damage sensitivity analysis (vary initial offset) ............................... 65  Table 9 Fatigue damage sensitivity (vary vessel length) ........................................... 68  Table 10 Fatigue damage sensitivity (vary simulation time) ..................................... 71  Table 11 Fatigue damage sensitivity (vary length per segment)................................ 72  Table 12 Omnidirectional wave scatter diagram prepared for 20 years period ......... 74  Table 13 Directional wave statistics prepared for 20 years period ............................ 75  Table 14 Occurrence matrix of directional wave for fatigue analysis (315⁰, 45⁰) .... 77  Table 15 Occurrence matrix of directional wave for fatigue analysis (45⁰, 135⁰) .... 77  Table 16 Occurrence matrix of directional wave for fatigue analysis (135⁰, 225⁰) .. 77  Table 17 Occurrence matrix of directional wave for fatigue analysis (225⁰, 315⁰) .. 77  Table 18 Displacement RAOs (Relative angle = 0 degree) ....................................... 92  Table 19 Displacement RAOs (Relative angle = 30 degree) ..................................... 92  Table 20 Displacement RAOs (Relative angle = 60 degree) ..................................... 93  Table 21 Displacement RAOs (Relative angle = 90 degree) ..................................... 93  Table 22 Displacement RAOs (Relative angle = 120 degree) ................................... 94  Table 23 Displacement RAOs (Relative angle =150 degree) .................................... 94  Table 24 Displacement RAOs (Relative angle = 180 degree) ................................... 95  Table 25 Wave load RAOs (Relative angle = 0 degree) .......................................... 103  Table 26 Wave load RAOs (Relative angle = 30 degree) ........................................ 103  Table 27 Wave load RAOs (Relative angle = 60 degree) ........................................ 104  Table 28 Wave load RAOs (Relative angle = 90 degree) ........................................ 104  Table 29 Wave load RAOs (Relative angle = 120 degree) ...................................... 105 

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Table 30 Wave load RAOs (Relative angle = 150 degree) ...................................... 105  Table 31 Wave load RAOs (Relative angle = 180 degree) ...................................... 106 

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Content Abstract ....................................................................................................................... v  List of Figures ............................................................................................................ vi  List of Tables ............................................................................................................. ix  Content ........................................................................................................................ 1  1. 

Introduction ........................................................................................................ 3 

2. 

Aims of the Project ............................................................................................. 7 

3. 

Critical Review ................................................................................................... 8 

4. 

Motions of FPSO .............................................................................................. 12 

5. 

6. 

7. 

8. 

4.1. 

Displacement RAOs ................................................................................... 12 

4.2. 

Wave Load RAOs ...................................................................................... 12 

4.3. 

Wave and Wind Drag force........................................................................ 13 

4.4. 

Stiffness, Damping and Added Mass Loads .............................................. 14 

Motions of Riser ............................................................................................... 17  5.1. 

Tension Force ............................................................................................. 17 

5.2. 

Bending Moment........................................................................................ 20 

5.3. 

Pipe Stress .................................................................................................. 20 

Example Calculations ...................................................................................... 22  6.1. 

Static Analysis............................................................................................ 22 

6.2. 

Dynamic Analysis ...................................................................................... 25 

Recommended Practices for the Design ......................................................... 30  7.1. 

Stress Element ............................................................................................ 30 

7.2. 

von Mises stress ......................................................................................... 31 

7.3. 

Allowable Stress ........................................................................................ 32 

7.4. 

Collapse Pressure ....................................................................................... 33 

7.5. 

Fatigue Life of Riser .................................................................................. 34 

7.6. 

Rainfall Counting ....................................................................................... 35 

7.7. 

S-N Curve .................................................................................................. 35 

7.8. 

Fatigue Life ................................................................................................ 36 

Case Studies ...................................................................................................... 37  8.1. 

Overview of the Project ............................................................................. 37 

9. 

8.2. 

General Information about the Timor Sea ................................................. 39 

8.3. 

Waves Statistics in the Timor Sea.............................................................. 41 

8.4. 

FPSO Simulation Model ............................................................................ 46 

8.5. 

Riser Simulation Model ............................................................................. 49 

Sensitivity Analysis .......................................................................................... 56  9.1. 

Sensitivity Analysis: Outside Diameter ..................................................... 57 

9.2. 

Sensitivity Analysis: Riser Length ............................................................. 60 

9.3. 

Sensitivity Analysis: FPSO Initial Position ............................................... 64 

9.4. 

Sensitivity Analysis: FPSO Size ................................................................ 67 

9.5. 

Sensitivity Analysis: Simulation Time ...................................................... 71 

9.6. 

Sensitivity Analysis: Length of Segment ................................................... 72 

10.  Probabilistic Fatigue Life ................................................................................ 73  10.1.  Waves for Fatigue Calculation ................................................................... 73  10.2.  Cumulative Stress Probability Distributions .............................................. 78  10.3.  Fatigue Life Probability Distributions ....................................................... 79  11.  Discussion .......................................................................................................... 81  12.  Conclusion......................................................................................................... 82  13.  Recommendations ............................................................................................ 83  Reference................................................................................................................... 84  Appendix I: Plots of Displacement RAOs .............................................................. 85  Appendix II: Tables of Displacement RAOs ......................................................... 92  Appendix III: Plots of Wave Load RAOs .............................................................. 96  Appendix VI: Tables of Wave Load RAOs ......................................................... 103  Appendix V: Wave Scatter Diagrams .................................................................. 107 

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1. Introduction Over the next decades, the world’s energy needs will double whereas the existing hydrocarbon supply will significantly depleted since they were consumed vastly to support the world economic growth in the twentieth century. To survive in the future, the offshore industries will be more diverse to develop new technologies and to explore new assets in more challenging environment. The company corporation, sharing know-hows and the best practices across different disciplines will be emphasized in order to quickly invent new technologies greatly demanded in the future. One of the promising areas for the future oil explorations is the deepwater where water depth is much greater than depth along the continental shelf. The deepwater normally range from few hundreds meter to about 6,000 meter for very deep areas. Because of the greater depth and mostly situated in the harsh environment, the exploration and production of hydrocarbon in the deepwater required advanced engineering and the multibillions investment to develop the projects meanwhile risk involved especially in the exploration stage is very high. In last 10 years, oil companies and drilling companies further out the sea to reach the last remaining oil reserves which are believed laid under the deepwater. A deepwater drilling used to be very dangerous and expensive activities in 20th century, but they seem suited in the current years. Also, the great energy demand from developing countries leads to the higher oil price which makes deepwater project become feasible and contributed to a renewed interest in further offshore explorations. For example, Gulf of Mexico is the deepwater region where deepwater drilling is very intense. According to the US Minerals Management Service (US MMS), there are 31 rigs drilling deepwater wells in the Gulf of Mexico in 2008 – compared with only 3 rigs operating in 1992. Seven gigantic deepwater projects come on stream in the US in 2008 including Thunder Horse field which is the largest field in the region. As well the deepwater exploration and production have continued in other regions in several corners of the world including Brazil, Angola, Nigeria, Australia, India, Indonesia, Australia and etc. However, most of deepwater oil has been found at the

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great extent in the goolden triang gle area whhich made up u of Mexicco, Brazil annd West Africa. Ex xxon Mobil, as claims to be the laargest comppany in deep pwater prodductions, says that the t deepwatter explorattion has beggun in only half of the know fieldds and in the future the deepwaater oil willl become more m significcant proporrtion of the total oil consumptiion.

Fiigure 1 Worrld map of the t deepwatter oil explo oration and production. p . Surface faacilities andd subsea tiebbacks in thee Gulf of Mexico, M Wesst Africa annd Brazil have been n tripled in numbers n of producing platforms inn last 5 yeaars. And, in the next 5 years, 66 6 potentiall deepwaterr platforms will be innstalled in major m regioons. The floating production platforms p innclude the storage andd offloading vessels (FPSOs), tensioned led platforrm (TLP), semisubmer s rsibles (SEM MI) and SP PAR whichh are the preferablee types for the ultra-deepwater. The T differen nt types off floating platforms p refer to thhe distinctivve requirement in the different d envvironment. In Gulf of Mexico, SPAR andd TLP typess are being chosen as common c opttion because the extrem me wave height in the t hurricanne season, while w FPSO Os are very engaging in i Brazil annd South Africa duee to the advvantages off the platforrm mobility y saving thee project invvestment significanttly for margginal oil fiellds.

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As water depth increase, so do the drilling and completion cost as well. Therefore, the next challenges are to minimize the cost of drilling, increase well productivity and developing technologies suitable for the deepwater environment. The techniques such as multilateral well, smart well completion, and extended well were developed by universities and famous research centers to make drilling and completion simpler and cheaper. Another importance issue is the platform stability in order to survive in unpleasant sea conditions. Generally speaking, TLPs have a practical limit of a 1,500 meter water depth, so for the deeper water the choices will be SPAR, FPSO or SEMI. The production riser is another main challenge for subsea engineers. In the deepwater, the hydrostatic pressure and temperature are tremendous obstacles for the oil production because they can causes of riser integrity problems such as riser collapse, cracking and fatigue damage. Hence, several types of riser are constructed to suit with the different the water depth, floating platforms and sea environment. The first and simplest riser system used in deepwater is the steel catenary riser system which the riser is manufactured from the steel tube painted with the anticorrosion chemicals. The Steel Catenary Riser (SCR) has been extensively used in deepwater operations because the cost of material and installation is significantly less than using flexible riser. Therefore, SCR has been vigorously demanded by the deep water development especially where the spool base for flexible riser is not available in that region. Besides, the SCR system is remarkable for its reliability, simplicity and robustness which make it as the first choice for the high pressure-temperature in deepwater applications. The Steel Catenary Riser is a simple riser system made of continuous rigid pipe. It must be installed from a floating structure and gently laid to the seabed. At the top end, the riser is connected with a flexible joint which is an equipment to allow small angular movement which makes the riser be less restricted to avoid excessive bending moment occurred at the outer rim. At the bottom end, the riser gradually touches the sea bed. The touchdown is known as a critical part on riser because it is where usually subjected with the maximum bending stress so as to the potential of crack and leak are high. The riser failure must be avoid in all means because

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consequences are extremely destructed. For the business, it brings in the complicated repairing program and reduction of companies’ revenue. For environment, it causes seriously environmental strains by the spilling hydrocarbon to the nature. Hence, industrial standards for different riser applications are established and enforced to the new deepwater projects. In addition, engineers have been developing a better, more accurate and reliable methods for designing the riser. The study will investigate possibility and perform the preliminary engineering design to make some recommendation for the PTTEP deepwater project in Timor Sea.

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2. Aims of the Project The objective is to discover the optimal design configurations for the riser and also to estimate the fatigue life by using a probabilistic approach. A gas export riser connected with the internal turret FPSO will be modeled to investigate the stress on riser which the stress will be induced by the FPSO motions. The industry practices for the riser design (API 2RD) are applied in the study to ensure the feasibility of being carried out. The important requirements specified in API 2RD such as the allowable stress, allowable deflection, hydrostatic collapse and fatigue life will be strictly followed. In addition, the study will investigate on how key design parameters such as riser diameter, wall thickness, riser length and FPSO’ size can affect the overall of riser design. The principle stress such as tensile, bending and hoop stresses will examine along the length to identify the critical segment. Afterwards, the fatigue damage will be calculated by using the S-N curve and rainfall half-cycle methods and combined fatigue damage of all sea states by the Minor’s rule. Lastly, a distribution curve of stress and fatigue life will be established.

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3. Critical Review The steel catenary riser has been adopted for many deepwater development projects developed on floating hosts in the North Sea and Gulf of Mexico (GoM). The experience in these area show that the fatigue problem is the most challenging issue for the riser design particularly true for a large diameter riser. The loading fatigue damage is directly related to the combined effect of various parameters such as environment condition, fluid density and water depth. Also, the riser design is very sensitive to motion characteristics of the host platforms. In ultradeepwater, the combined mass of the mooring lines, risers and umbilical have a great proportion to the total mass and drag force of the system. So, in the past, the riser and vessel motions will be analyzed by the uncoupled method where the FPSO motions will be calculated separately from riser. The results of FPSO motion then will be applied as initial conditions for the analysis of the riser motions. However, this method seems associated with huge error in hydrodynamics damping force and the resonant responses of the system. As described in the motion studies performed by J. Xu in 2006, he suggests that the restoring stiffness of mooring and riser, mass and viscous damping will change the roll and pitch frequency as well as the slowly varying drift motions. In the riser design, the characteristics of the floater have strongly link with the dynamic of the riser. The main interfaces are such as hang-off locations, flexible joint, stiffness of the mooring system and maximum heel, yaw and pitch of the vessel in survival conditions. These factors are not exhaustive, and a numbers of piece of information must be collected and exchanged along with the designing phase of riser and floater. The riser design is the result of compromises between tension at the top, maximum bending stress at the touchdown point and risk of the collision with nearby structures due to lateral displacement. In most case, the tension needs to be minimized in order to reduce the hang off load, limit impact to the mooring system and minimize horizontal load at the touchdown point to prevent slipping of flow line.

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However, the tension is limited by the demand of size and length of riser as well as the lateral tension required for suppressing the bending stress at the touchdown point. If the analyses are well understood and easy to perform, the riser configuration will be easy to verify. Also, the fabrication and installation method should be done without difficulty. However, at every step of calculations, there are uncertainties involved which have significant impact on the riser configuration such as actual pipe thickness, installation tolerance for subsea equipment, uncertainties in the measurement of the position of the floater, uncertainties of the water depth, sea condition variations and etc. The consequence of all these uncertainties should be analyzed carefully especially the sections included special characteristic; for example, different wall thickness, steel grade and welding method. In the dynamic condition, several parameters can affect to the riser motions such as the first and second order motions of the vessel, length of riser and sea conditions which they could make the touchdown point shift vertically and horizontally. During the movement, the riser is subjected to additional axial stress making the touch down region highly sensitive to the fatigue failure damage. Also, the platform motions will cause changes in the departure and curvature of the riser, which leads to significant excessive bending stress. Different methods and tools to analyses the riser’s behavior were invented to combat these challenges and to perform the riser design in the time frame of a project.

The extreme analysis of riser, where wave loads based on maximum wave height, is another essential study for the riser design. However, the calculation of extreme wave height is subjected to a large numbers of errors. First, errors arise in the data collection due to malfunction or inaccuracy of the either equipment or method of measurement. Second, the long-term distribution to describe wave characteristics maybe not selected appropriately. The criteria for selection are theoretically various and still unclear. In other means, no reason is to select one particular distribution to describe the wave nature over another. Most of the time, it is often based on the judgment of engineers. Last is an uncertainty from insufficient collected wave data. Because the prediction has extrapolated 20, 50 or 100 years exceed from the service

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life, but usually only a few years data collection can be gathered when starting the design. Therefore, it is clear that a high degree of uncertainty is surely expected in the calculation results. In addition, the accuracy results require the time domain analysis of wave frequencies as well as quasi static offset of the system. In such analyses, they are CPU time consuming process which is in general not applicable in the earlier design stage. Therefore, some shortcuts are necessary to be applied; for example, the vessel motions induced by low frequencies wave and the mean environment loads are defined as a static initial offset of the vessel. Another necessary analysis for riser is the fatigue analysis, especially the case of the large production riser. There are two places on riser prone to the fatigue failure. First is the touchdown point where the bending stress is the highest. Second is the first welding seam below the flexible joint, where the maximum axial stress is occurred. Since there are several uncertainties involved in the calculations, several methods come up in order to achieve higher accuracy for the results. The recent attempts to manage the uncertainty contained in the calculation of probabilistic fatigue life is introduced by Wirsching (Wirsching, 1984) and recently emphasized by Tapan (Tapan K Sen, 2008). However, the study did not embrace the effect of low frequency excursion (slow drift motion), torsional stress and VIV. Also, the random nature of waves which have immense effect on the stress of riser is limited to single directions because the limitation of software used at that time (Virtual Orcaflex 2001). Tapan simulated a typical FPSO operating in the West Africa where water depth is around 1,200 meters. Sea states data are compressed to a number of equivalent wave height and time crossing periods (Hes and Tez) in order to reduce the numbers of cases and time for simulations. Waves are categorized by the wave height which the equivalent wave height (Hes) is calculated by using weighted average with H6 for any waves having the same time crossing period (Tez). This approximation is due the fact that stress is proportional to square of wave height (H2), and fatigue damage is approximately proportional to the third power of the stress range (S3).

Tapan simulated the stress time history at a node near the

touchdown point to analyses the stress ranges and return periods by using traditional rainfall counting method. After that, the fatigue life is done by using Monte Carlo

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Simulation with the probability assigned to input parameters e.g. wall thickness, eccentricity, stress range and stress concentration factor. In his study, the nondirectional wave data was utilized to avoid large number of load cases. However, the lack of wave direction data may result in an unacceptable high uncertainty of the simulation results.

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4. Motions of FPSO 4.1. Displacement RAOs The FPSO motion can be described by a displacement RAOs (Response Amplitude Operators). The RAOs consist of pair of numbers to define responses in 6 DOFs (surge, sway, heave, roll, pitch and yaw) of a particular wave period in a certain wave direction. The RAOs are composed of the response amplitude (R) which defines the response when the FPSO exposed to 1 meter wave height. Another component is the phase difference to define a lagging or leading phase of FPSO relative to the approaching wave. The RAOs are strongly related to the shape, size and draught of FPSO normally obtained from the hydrodynamics experiment or the simulation. The RAOs can be expressed mathematically by using the following equation. x  R  a cos( w t -  ) .................................... (1)

where x = vessel displacement (m) R = RAO Amplitude (m) a = wave amplitude (meter) ω = wave frequency (rad/s) t = time (second) φ = phase difference between wave and FPSO responses (rad)

4.2. Wave Load RAOs Force and moment can be represented by wave load RAOs in the same manner as the displacement RAOs. In the simulator, the force and moment from wave load RAOs will be combined with other loads to describe the motion by using the Newton’s law of motions. Because the wave load RAO consists of force and moment, their unit are Newton and Newton-meter per wave height respectively.

Force  RF  a cos(t ) ................................(2)

Moment  RM  acos(t ) ..............................(3)

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where R F = wave load RAOs (N) R M = wave moment RAOs (N) a = wave amplitude (meter) ω = wave frequency (rad/s) t = time (seconds) φ = phase difference between wave and FPSO responses

4.3. Wave and Wind Drag force Hydrodynamic drag is an important force component for modeling the FPSO motion especially the slow drift motion. Drag forces can be modeled with a relation of the relative velocity, yaw rate and roll rate.

Drag force due to Relative Velocity Drag force due to water or wind flowing toward the buff body will be calculated by substituting the velocity relative, drag coefficient

and projection area into the

equations which express drag forces in surge, sway and yaw directions. 1  wCSurge ASurgeV 2 2 1 FSway   wCSway ASwayV 2 ................................(4) 2 1 M Yaw   wCYaw AYawV 2 2 FSurge 

where ρ w = density of water or air (kg/m 3 ) C = drag coefficient in the direction respected to vessel heading A = projection area in surge, sway and yaw (m 2 ) V = relative velocity of the water or air past the vessel (m/s)

Drag force due to Yaw Rate For wind drag, the yaw rate term is insignificant and will be omitted from the calculations; but it is still influential for wave drag to describe the motions of FPSO. The drag due to yaw rate can be expressed by the following formula.

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1  w   K Surge 2 1 FSway   w   K Sway .................................(5) 2 1 M Yaw   w   K Yaw 2 FSurge 

where F = drag force (N) ρ w = density of sea water (kg/m 3 ) ω = yaw rate (rad/s) K = damping coefficient (s/m)

Drag force due to Roll Rate As similar as the yaw rate term, the row moment is modeled by using the equation defined in the following.

M Roll  KLV  KQV V ..................................(6) where MRoll = moment due to roll rate (N  m) V = angular velocity component (rad/s) KL = linear roll damping coefficient KQ = quadratic roll damping coefficient

4.4. Stiffness, Damping and Added Mass Loads The stiffness, damping coefficient and added mass and are important hydrodynamic variables for evaluating the FPSO motions. These parameters refer to the forces which are described in the following.

Stiffness Load Force due to stiffness occurs when the vessel is offset from the equilibrium position. The stiffness (heave, roll and pitch) can be represented by the stiffness matrix and it

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is a function of vessel type, draught and water plain area shown by the following equations.

 FHeave  OHeave  M   K  O   Roll   Roll  ....................................(7) M Pitch   OPitch  where F = hydrodynamic stiffness force (N) M = hydrodynamic stiffness moment (N-m) K= hydrodynamic stiffness (N/m) O = offset from equilibrium position (m)

Damping Load The damping load is equal to -D*V, where D is the specified damping matrix and V is the vector of FPSO velocity relative to the stationary. The damping loads are calculated by using the following matrix equation.

 FX  VX  F  V   Y   Y  FZ   VZ     D   ......................................(8) M X  X   MY  Y       M Z  Z  where F = hydrodynamic dampling force (N) M = hydrodynamic damping moment (N-m) D = damping coefficient (s/m) V = velocity (m/s) ω = angular velocity (rad/s)

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Added Mass Load The added mass load is calculated as similar as the damping loads, but the added mass matrix is used instead of the damping matrix.

VX   FX    F   VY   Y   VZ   FZ     M ADD   ...................................(9)  X  M X     MY   Y   M  Z   Z  where F = hydrodynamic dampling force (N) M = hydrodynamic damping moment (N-m) MADD = added mass coefficient (kg)  = linear acceleration (m/s 2 ) V  = angular acceleration (rad/s2 ) ω

16

5. Motions of Riser In the simulation, a riser is divided into a series of line segments which are then modeled by straight-massless model where each segment will have node at each end. The segments will represent axial and torsional stresses occurred in the riser. On the other hand, properties such as mass, weight and buoyancy will all lump to the nodes. A line segment is divided into two halves and the properties such as mass, weight, buoyancy and drag coefficient of each half‐segment will be lumped to the node at the segment end. Forces and moments are calculated in 4 categories and applied at the nodes. 1. Tension Forces 2. Bend Moments 3. Circumferential force 4. Shear Forces (neglected due to insignificant magnitude)

5.1. Tension Force The tension of each segment is calculated by using the linear stiffness assumption. In this case, the linear axial stiffness represents the axial spring and damper at the center of each segment. A mathematic expression for the tensile force is described below.

Te Tw (PA o o  PA i i ) ..................................(10) Where Te = effective tension  kN  Tw = wall tension  kN  Pi = internal pressure  psi  Po = external pressure  psi  A i = internal cross sectional stress (m 2 )

17

The wall tension (Tw) is tension on the riser measured at the pipe’s circumference. It consists of three main components. First is the elongation tension in axial direction, the second is the tension due to the line pressure effect and the last is due to the damping effect. The wall tension can be described by the following equation.

Tw = EA  2 (Po Ao -PA i i) 

EA.e  dL     ..................(11) Lo  dt 

Where EA = axial stiffness (kN/m) ε = total mean axial strain = (L - λL0) / (λL0) L = instantaneous length of segment (m) λ = expansion factor of segment L0 = upstretched length of segment (m) ν = poisson ratio Pi, Po = internal pressure /external pressure (psi) Ai, Ao = internal / external cross sectional areas (mm2) e = damping coefficient of the riser dL/dt = rate of changing of riser’s length (mm/s)

18

F Figure 2 Seg gments and nodes in riser model. a wall To undersstand the foormula andd the differeence betweeen effectivve tension and tension, coonsider the forces acting axially at a the mid‐ppoint of a segment. s Thhe nodes either sidee are to reppresent a len ngth of pipee plus its coontents. Moore importaantly, the forces on them are caalculated as if the lengtth of pipe reepresented had h end capps which e to the internal and extern nal pressuree. The figurre below hold in the contents exposed ure forces. illustrates the tensionn and pressu

Fiigure 3 Walll tension annd pipe presssure force.

19

5.2. Bending B Momen nt In case off linear bennding, the formula f is based on the t isotropic bending stiffness bending which meeans the x-- and y- bending b stifffness are identical. Therefore, T moment can be calculated by usiing the beloow equation n.

M oment  EI E C  D

d C

...............................(12)

dt

Where EI = bendiing stiffness (N. m2) D = bending dampingg value for a segment (N-sec) C = curvatture of segm ment (m) t = time (ssec)

5.3. Pipe P Strress The stresss calculatioon will be applied a by a simple cylinder c whhich the insside and outside diaameters aree given. Thee cylinder iss assumed to t be made of uniform material which can n be either steel s or titannium riser. When conssider a cross-section off pipe as shown in the following diagram m, the framee of referencce has an origin o locateed in the centerline where Oz is the direcction along the pipe ax xis. In addittion, Ox andd Oy are normal to the pipe axxis in the crooss-sectionaal plane.

Figurre 4 Frame of o referencee of pipe streess calculattion. a point P, which can be identifieed in the pip pe section. A local sett of axes Consider at (R, C, Z) where w R is radically ou utwards, C is i in the circcumferentiaal direction and Z is

20

parallel to the axial direction. Regarding to these axes, the stress component at P is 3x3 matrixes which will be given by

 RR  RC  RZ  RC CC CZ .......................................(13)  RZ CZ  ZZ The diagonal entries of the matrix RR, CC, ZZ are the principle stress for radial, hoop and axial stresses respectively. The other 6 off-diagonal components are the shear stresses in 3 dimensions. However, the diagonal stress components are considered as insignificant for the stress and fatigue damage; therefore they will be disregarded in this study.

21

6. Exxamplee Calculations 6.1. Static S An nalysis The staticc analysis is perform med to obtaain the riser position n in the sttationary condition. In this exaample, the stteel riser is deployed to o 1000 metter water depth. The e diviided to 4 seegments byy using the lumped maass method.. By this length is equally means, thee segment properties p a specifieed into the each are e node. The hydroddynamic forces e.g.. wave and wind drag force f will be ignored in n this stage in order to simplify the calculaations. Neveertheless, thhese forces will be takeen into calcuulations in O Orcaflex simulation n to obtain better b accuracy and reliiability.

Figure 5 Free-boddy diagrams for FPSO and a riser sysstem.

22

Figure 6 Wave forrce RAOs ffor surge and d heave mootions

23

24

Figgure 7 Estim mate riser prrofile in stattic conditionn.

6.2. Dynamic D c Analysis The dynaamic analyssis is perfoormed to innvestigate the motionn, force annd stress occurred in i the riser in dynamicc situationss which gennerated by the t excitatioon force from wavves and FPS SO. In the dynamic annalysis, the von Misess stress is a critical design critterion for riser because the riser stress s will be b limited by b its yield strength after multtiplied withh the safetyy factor. Heence, the deesign must be ensure that the stress is always a undder the recoommendatioons in all conditions. c In the exaample, it presents how h the calcculations aree done for the t node dissplacement, elongation, tension and stress when 1 m wave w of 8 second returrn period appproaches att the bow off FPSO.

25

26

Figure 8 Nodes N displlacement in X-axis.

Figure 9 Nodes N displlacement in Y-axis.

27

28

Figuree 10 Tensilee stress proffiles for each h riser segm ment.

29

7. Recommended Practices for the Design The API 2RD design practices are widely used in the offshore industry to provide the guideline for the safe and practical design. The critical design parameters are such as maximum stress, bending moment, hydrostatic collapse and the fatigue life which will be explained more in this chapter.

7.1. Stress Element Three principle stresses will be investigated at the critical sections along the length of riser to ensure that the principle stress is under the allowable quantity. For plain cylinder riser, the principle stress will be classified as one of the following. Table 1: Stress definition according to API 2RD Any normal or shear stress that is necessary to have static equilibrium Primary

of the imposed forces and moments. Thus, if a primary substantially exceeds the yield strength, either failure or gross structural yielding will occur. p is the average value across the thickness of solid section excluding the effects of discontinuities and stress concentrations. For example, the general primary Membrane membrane a loaded in pure tension is the tension divided by the cross- sectional area. p may include bending as in the case of simple pipe loaded by a bending moment. b is the portion of primary stress proportional to from Bending

centroid of a cross section, excluding the effects of discontinuities and stress concentrations.

q is any normal or shear stress that develops as a result of material Secondary

restraint. This type of stress is self-limiting which means that local yielding can relieve the conditions that cause the stress, and a single application of load will not cause failure.

30

7.2. von Mises stress For plain round pipe, where transverse shear and torsion are negligible, three principal stress components of primary membrane stress will be equivalent to von Mises stress. The equation is showed in the equation below.

e 

1 2

( pr   p ) 2  ( p  

pz

) 2  (

pz



pr

) 2 ..........(14)

where σe = von Mises equivalent stress, N/mm2 σ pr = principle stress in radial direction, N/mm2 σ pθ =principle stress in hoop direction, N/mm2 σ pz = principle stress in axial direction, N/mm2 For a thick walled pipe, the principle stress will be derived from the following equations

 pr 

-(Po Do +Pi Di ) Do +Di

 p  ( Pi  Po )  pz 

Do  Pi .................................(15) 2t

T M  ( Do  t ) A 2I

where Pi = internal pressure, N/mm 2 Po = external pressure, N/mm2 Do ,Di = outside,inside diameter, mm t = pipe wall thickness, mm A = crosssection area, mm 2 T = wall tension, N M = bending moment in pipe, N-mm I = moment of inertia, mm 4

31

7.3. Allowable Stress Regarding to the API 2RD for a plain pipe, the von Mises stress should be less than the allowable stress defined by the product of the design case factor (Cf) and the allowable stress (σa).

(

p

)e  C f 

a

.........................................(16)

where σa = Ca .σ y = allowable stress σ y = material minimum yield stregth Ca = allowable stress factor, Ca = 2

3

C f  design case factor Table 2 Design matrix for rigid risers Design

Load

Environmental

Case

Category

Conditions

Pressure

Cf

1*

Operating

Maximum operating

Design

1.0

2

Extreme

Extreme

Design

1.2

3

Extreme

Maximum operating

Extreme

1.2

4

Extreme

Maximum operating

Design

1.2

5

Temporary

Temporary

Associated

1.2

6

Test

Maximum operating

Test

1.35

7

Survival

Survival

Associated

1.5

8

Survival

Extreme

Associated

1.5

9

Fatigue

Fatigue

Operating

N/A

32

7.4. Collapse Pressure Riser design must be ensured that it will not be collapsed during any operations. Therefore, the riser should be able to withstand hydrostatic pressure at any time during installation, production as well as workover. The effect of variations in pipe thickness, ovality, eccentricity and residual stress from pipe manufacturing should be included in the pipe collapse pressure. The allowable collapse pressure and collapse pressure for round pipe can be calculated by using the following formula.

Pa  D f Pc

...........................................(17)

where Df = collaspe design factor (0.75 for seamless or ERW pipe) Pc = collaspe pressure (psi) Pc 

Pe Py (Pe2  Py2 )

.......................................(18)

where D,t = nominal pipe outside diameter and wall thickness (mm) D max = maximum outside diameter of pipe (mm) D min =minimum outside diameter of pipe (mm) E,υ = modulus of elasticity and Poisson's ratio (N/m 2 ) σ y = specified minimum yield stress (N/m 2 ) A = cross secional area of pipe (m 2 ) a = cross sectional area of wall (mm 2 ) Te = effective tension (N) G = unit weight of water (kg/m3 ) H = water depth (m) Pi = internal pressure (psi) P = net external pressure = GH-Pi

Sa = mean axial stress = (Te -PA)/a -Pi





Yr = reduce yield stress = σ y 1-3(Sa /2σ y ) 2  -  Sa /2σ y  1/2

Py = yield pressure with simultaneous tension =2Yr t/D Pe  elastic buckling pressure = 2E/(1- 2 )(t / D )3

33

For a pipe designed to meet the external collapse criteria outlined above, collapse will be initiated at a lower pressure by accidents e.g. impact or excessive bending due to tensioner failure. The maximum allowable collapse pressure will be done using the formula below to ensure the pressure differential will be less than the predicted propagation pressure.

Pd  D p P p

...........................................

(19)

where Dp = collaspe propagation design factor = 0.72 Pp = collasse propagation pressure=24σ y (t/D)2.4

7.5. Fatigue Life of Riser The fatigue damage in riser comprises of several contributions such as vessel motions, direct wave loads, transportation and VIV. Damage due to vessel motions can be further split into that due to the wave-frequency and the slowly-varying motions. The former refers to the small in the stress magnitude but comparatively rapid in the return periods. Whereas the latter can be perceived as an enormous in magnitude, but less frequent in term of return period. In the API practices, the design fatigue life should be at least 3 times greater than the service life (SF ≥ 3). This recommendation will be applied for any locations that the safety and pollution risk are low and the regular inspection is possible. On the other hand, for locations where the riser cannot be inspected regularly or the safety and pollution risk are highly concerned, the design fatigue life is recommended to be at least 10 times the service life (SF ≥ 10). In this study, the environment in the Timor Sea is considered as a tolerable condition which the regular inspection and maintenance can be performed regularly. Therefore, the design factor of 3 will be used to evaluate the riser design in this project.

Service life  Design factor×Fatigue life .............. (20)

34

where Design factor = 3.0 Service life = 15-20 years

7.6. Rainfall Counting The rainfall counting technique is used to analyze the stress time history and present it in form the stress range and the time crossing period. With this technique, the fatigue damage created by different sea states can be integrated by using Minor’s rule which is very effective way to analyze fatigue damage in complicate structures.

7.7. S-N Curve An S-N curve defines cycles to failure of structures subjected to cyclic loadings. The S-N curve can be derived from either direct experimental or follow the API recommended numbers. Generally, the API Class X is a recommended code for the riser design and it can be expressed by the following equation.

N  A (SCF  )m ...................................(21) where N = cycle to failure (cycles) S = stress range, (MPa) m = empirical numbers Table 3 S-N curve parameter for API Class-X APIClass-X

A

2.50*10 13

m

3.74

SCF

1 .0

35

Figure 11 SN curvve (API Classs X).

7.8. Fatigue F L Life From the S-N curve,, the annuaal fatigue daamage will be accumuulated by using u the Minor’s ruule. Therefoore, fatigue life is the reverse r of tootal damagee in one yeaar which is shown below. b

D FL =

n .............................................(22) N 1

D

............................................(23)

where D = fatiguue damage (%/year) FL = fatiggue life (yeaar) n = numbbers of stress cycle in 1 year N = numbbers of stresss cycle to failure f

36

8. Casse Stud dies 8.1. Overview O w of the Project The objecctives of thee study aree to identifyy the criticaal section, seek the opptimized design and estimate fatigue lifee of the steeel catenaryy riser. Thee study staarts from constructioon the FPS SO model in n Orcaflex to represennt a typicall FPSO useed in the Timor Seaa, West Ausstralia. The most likelyy sea states will be useed in the sim mulation to investigate the sttress profilees and ideentify the critical c poinnt on the rrise and sensitivityy analysis will w be performed to seeek the optim mized configgurations. Next, the extreme wave w load will w be geneerated to ob bserve the tensile t and bending he critical segment. s Inn this case, the FPSO is assumed d to be ablee to drift stress at th away +/- 10% of thhe water depth d from the mean position. Inn addition, several d sim mulation tim me and nuumber of parameterrs, such as FPSO sizee, drifting distance, nodes willl be changed to obsserve the impacts i to the fatigu ue damage. Lastly, individuall wave dataa will be claassified intoo bins whichh are createed for certaain range of wave height. The probability p based on thhe statisticall wave dataa will be asssigned to the wave bins. b After that, 4 wavve trains from 4 directio ons will be simulated to t create excitation force at thhe FPSO. Lastly, L the fatigue f life distribution n will be pllotted to find the mean m fatiguee life of riserr.

Figure 12 Block B diagrram represennts the apprroach for prroject (1).

37

Figure 13 Block B diagrram represennts the apprroach for prroject (2).

Figure 14 Block B diagrram represennts the apprroach for prroject (3).

38

8.2. General Information about the Timor Sea The Timor Sea is the relatively shallow sea bounded from the north by the Timor Island, from the south by Australia and from the west by the Indian Ocean. Beneath, considerable oil and gas reserves are laid. Nowadays, numbers of offshore production platforms and drilling rigs are in operations in the shallow water depth areas and also trench in the deepwater regions. Montara field is an oil development filed operated by PTTEP Australasia in the shelf region of the Timor Sea. This field is situated 250 km southwest of the Timor Island and 685 km west of the Darwin city in Australia. The metocean data have been collected extensively in Montara and Jabiru field which is another field nearby. The measuring data provides the fundamental information about wind, wave and current

which are essential to evaluate the riser design. For the Timor Sea, key oceanographic features are listed below. 

The Pacific-Indian ocean flow likely generates persistent west to westsouth currents.



The monsoons are the controlling factor of metocean in the Timor Sea for the short return period wind and wave. Tide is a dominant factor to control the oceanic current.



The Coriolis’ effect is comparatively weak due to the low latitude and the tropical cyclones are likely immature. However, small but intense tropical cyclones could control the long return period waves and winds.

39

Figgure 15 Loccation of Moontara field, Timor Seaa.

mor Sea (waater depth > 500 Meters). Figuure 16 Deepp water areaas in the Tim

40

Figure 17: Existing developm ment fields in n the Timorr Sea.

8.3. Waves W Sttatistics in the T Timor Seea No specifi fic wave meeasurementss existed in the Montarra area. Thee best availaable and most appropriate meaasured wavee data for thhe Montara Field is thee data in Jabbiru field t northeaast ~75 Km m). Most of the data taaken are om mnidirectionnal wave (away to the data recorrded in 2, 3,, and 4 hourrly intervalss. The meassurement is done over 10 years from Octoober 1983 too January 1993, but thee full year of o directionnal wave datta which will be useed in the stuudy is availaable only frrom Decembber 1995 – December D 1 1996.

41

Wave Climate The ambient wave climate for the Montara field is composed of separated sea and swell waves, with a wind-sea/swell separation of 9 seconds (0.111 Hz) found from the plotted Jabiru wave spectra. The combination using the square root of the sum of the square wave height results in the total waves.

Hstotal 

Hs 2 sea  Hs 2 swell ..............................(24)

Sea Waves Sea waves are waves locally generated by wind. As such, the sea wave climate is very closely allied with the summer westerlies and winter easterlies. Transient variations to these persistent seasonal regimes are caused by the various storm types, which occasionally affect the region. As a result of the very long fetched storm, sea waves may have periods ranging from 2 or 4 seconds to as long as 6 or 8 seconds.

Swell Waves Surface wind waves which are generated by remote storms (i.e. 400 - 7000 km away) and propagate to a site independently of the storm, are known as swell. In the Southern Hemisphere, swell results predominantly from storms in the Southern Ocean or the southern portion of the Indian Ocean. After generation, swell may propagate towards the equator, gradually dispersing and decreasing in amplitude before arriving at the Timor Sea from the southwest. Since longer period swell suffer less dissipation, periods of long-travelled swell are usually greater than 14 seconds commonly ranging up to 20 seconds and occasionally exceeding 22 seconds. Shorter period swell (6 to 10 seconds), may result from tropical cyclones, and from winter easterlies over the Arafura Sea and eastern portions of the Timor Sea.

42

Figure 18 Swells from f south Indian I Oceaan to Timorr Sea.

Maximu um Singlee Waves Within anny sea statte characterrized by a particular significantt wave heiight, the maximum m individuall wave heiights (EHmaax) may bee up to twiice as highh as the significantt wave, witth correspoonding perioods ~10% longer than n the signifficant or mean wav ve period. The T formulaations of Goda G (1985)) for non-cy yclonic wavves have been emplloyed in thiss study.

EH max  1.86Hs ETmax  1.15Tm

.........................................(25)

Seasonaal Variability The monthhly variatioon in total wave w heightt, period andd direction are shown in detail in the wavve rose diaagrams. Thee wind wavves or sea waves will closely follow the monsoonaal wind direections, withh westerly seas s prevailling from December D too March, shifting to o predominnantly easteerly from April A to earrly Novemb ber, before shifting

43

back to thhe west. A very v small easterly winnd wave coomponent may m occasioonally be present in n the summeer months, possibly atttributable to t distant trropical distuurbances that generrally form to the east of the Montara M Fieeld. Throug ghout the year, y the predominaant swell diirection rem mains from the southw west (and to a lesser deegree the west). Som me shorter period p swelll will occassionally appproach from m the east inn winter. The mon nths with the smalleest waves are Marcch, Octobeer and Noovember correspondding to the calmest moonths for winnd.

Figure 19 Annual wavve rose diaggrams meassured at Jabiiru field.

44

Figure 20 Monthly waave rose diaagrams meassured in Jabbiru field.

45

Non-Cyclonic Storm Waves The summer and winter monsoonal and trade wind surges also generate the strongest non-cyclonic storm waves, which could be coupled with the perennial westsouthwest background swell component. It could result in the maximum noncyclonic total sea states. These non-cyclonic total sea states are the controlling storm type for the shorter return periods less than 5 years. Applying a minimum total significant wave height threshold of ≥ 2.7 m (annual), ≥ 2.7 m (summer) and ≥ 2.5 m (winter) to the measured ambient wave database in the Montara Field and excluding any tropical cyclone events resulted in the annual extreme events. These extreme wave events are then subjected to the Conditional Weibull extreme analysis technique. The corresponding parameters such as the extreme significant wave heights (Hs), return period mean wave periods (Tm), spectral peak periods (Tp) and average zero crossing periods (Tz) are derived from the storm peak correlations and shown in the table below. Table 1 Return period of non-cyclonic winds, waves and currents in Montana field Non‐Cyclonic Annual Return  Periods

Parameter

Unit

Significant Wave Height

Hs

Spectral Peak Wave Period

Return Periods (Yrs) 1

2

5

10

25

m

3.52

3.82

4.15

4.37

4.62

Tp

s

9.66

10.07

10.49

10.76

11.06

Spectral Mean Wave Period

Tm

s

7.4

7.71

8.04

8.25

8.48

Average Zero Crossing Period

Tz

s

6.75

7.04

7.33

7.52

7.73

Maximum Single Wave Height

EHmax

m

6.55

7.11

7.73

8.12

8.59

Period of Maximum Wave

THmax

s

8.52

8.87

9.25

9.48

9.75

8.4. FPSO Simulation Model The FPSO model is constructed based on information derived from an existing Montara FPSO and the specifications are described in the following table. For the hydrodynamic parameters such as the displacement and wave load RAO will be adopted from the typical ship-shaped FPSO. These detail information of FPSO’s hydrodynamic parameters will be provided in the appendix.

46

Figgure 21 Montara FPSO O.

47

Figure 22 Montara FP PSO specifi fications.

48

Figure 23 2 FPSO model m (Side view). v

Figure 24 2 FPSO moodel (Front view).

8.5. Riser R Sim mulation n Model The assum mption for the t riser is that X70 carbon c steell will be ussed to fabriicate the riser and steel s tubulaar will be manufacture m d by either the electricc-resistancee welded (ERW) orr double- suubmerged arc a welded (DSAW). The T materiaal specificattions are

49

assumed to conform with the established industry specifications for the minimum tensile strength, service temperature, fatigue resistance, internal corrosion and wear resistance. Table 4 Pipeline specifications Steel grade

X70

Outer diameter (13')

0.3302

(m)

Inner diameter (11')

0.2794

(m)

Mass per unit length

0.173

(te/m)

SMYS

70

Kips

Bending stiffness

4.60E+04

(kN.m^2)

Axial stiffness

4.66E+06

(kN.m^2)

Poisson ratio

0.293

To justify he pipe specifications above, calculation is made according to the API practices. The allowable stress in pipe, fracture toughness requirement, riser deflection, and collapse pressure and collapse propagation will be checked with the pipe properties. Below is the simulated case when 1 meter wave with about 6-8 second return period is approaching the FPSO.

Allowable Stress in Plain Pipe The figure below illustrates combined stress profiles from top to bottom of riser. The minimum, maximum and mean of von Mises stress are plotted in the graph in blue, green and black respectively. The red line is the limiting stress for steel pipe which is greater than the combined stress for every pipe section. The Riser API 2RP Utilization, reported as percentage of pipe stress over the allowable stress, is averaged at 0.4 with in a range of +/- 0.2. So, it proves that the purposed riser can withstand the typical sea condition.

50

Fig gure 25 Plott of maximuum von Misses stress annd allowablee pipe stresss.

Figgure 26 Plott of riser utiilization (AP PI RP 2RD)).

Minimum m Fracture Toughnesss The minim mum fractuure toughneess of mateerial shouldd be sufficieent to avoiid brittle fracture at a the expeected stresss level oveer anticipatted service life. The fracture mechanicss based connsiderationss are approopriate and more impoortance forr highlyloaded meembers suchh as the connnections annd welded seams. s In adddition, low w service temperatuure is anothher critical factor influuenced steel behavior to be moree brittle.

51

Therefore, the careful testing for steel toughness should be performed to compare the results between different testing methods. The testing procedures such as Charpy test, CTOD, drop weight tear test are standard test for steel used in the pipeline industry.

Riser Maximum Deflection The maximum riser deflection is specified to prevent the excessive high bending stress in riser which may cause riser leakage and failure. Even when the riser stress is under the manufacture’s recommended, the larger riser deflection is needed to be controlled to prevent multiple risers from interfering and crashing. Therefore, the riser system may include additional equipment such as tensioners, flexible connections and telescopic joints to provide bending and rotating abilities of the riser. These tools should be designed at the worse condition in the extreme case analysis. Two figures illustrated below indicated smoothly change of the curvature and bending radius of riser. The maximum bending stress occurred at 2000 meter where the riser is gently approaches the sea bed. The maximum curvature this particular point is averaged at 0.0006 rad/m which is the relatively low when compare with other stress component. Therefore, the planned riser configuration with this trajectory seems to be applicable in the real operations.

52

Figuree 27 Bendinng radius proofile.

Figuree 28 Riser cuurvature proofile.

Pipe Collaapse Pressu ure The criteriion for collaapse pressuure is that thhe external hydrostatic h pressure shhould not exceed the ability off riser to withstand w the hydrostattic pressuree experienceed in all operationss during thee service liffe. Theoretiically, the collapse c resistance is innfluence by severaal factors suuch as ability, eccentrricity, anisootropy as well w as the residual stress in material. So, S these vaariables ressult in trem mendous diifficulties too obtain

53

precise estimation off the collapsse pressure. However, in the pracctical way, collapse pressure of o riser is given g by Pc which is thhe multipliccation of th he allowablee design pressure Pa and the saafety factorr. The below w is examplle calculatio on for pipe collapse pressure.

54

Figure 29 Pipe collapsse pressure and the net hydrostatic pressure.

55

9. Sensitivity Analysis The sensitivity analyses are performed to investigate the relationship between key design parameters and the riser internal stress. Several parameters such as the outside diameter, riser’s length, initial position, FPSO size, simulation time and the length per segment will be examined in this study. The study excludes wave drift motion effect in order to avoid model complexity and enormous time required for simulation, but the study will focus more on the effect due to the heave and pitch oscillating motions because they are believed as the primary factors influence to the fatigue life. Table 5 Simulation parameters used in the base case Base case Steel grade

X70

SMYS

482E+3

kips

Wave height

1

m

Water period

6

sec

Wave direction

Bow

Water depth (d)

1000

m

Horizontal departure (X)

3000

m

Riser length (L)

3300

m

Half span (l)

1756

m

Internal pressure at z =0

2500

psi

Fluid in riser

Gas

Density of fluid

0.205

te/m^3

56

9.1. Sensitivit S ty Analyysis: Outtside Diaameter The purpoose of this study s is to iddentify the critical secttion and fin nd the optim mum size of riser which w is abble to resisst collapse pressure as well as minimizing m g fatigue damage. Inn this studyy, the OD is set up in 5 different caases with the OD increaase from 13.0 to 15.0 inches. From the results bellow, the sm maller OD is the largeer stress c sectiions are identified on th he riser. Thhe first is concentrattion. In adddition, two critical at the riserr top in whiich the tensiile stress is extremely high h due the suspendedd weight of the riseer. Next is thhe area arouund the touchdown point where thhe bending moment is highly elevated e beccause the risser is lifted off from the seabed. r 1 innch wall thickness (seee case 1) is the t approprriated choice for the From the results, design beccause it proovides sufficcient strenggth to withsttand the maaximum hooop stress occurred in i common sea states (allowable ( h hoop stress = 347 MPaa, using SF = 0.72). Although a thicker piipe will resuult in a less fatigue dam mage, a 1 inch thicknesss riser is still a preeferable chooice because its can provide p suffficient fatiggue life (111 years) which is much m greateer than expected field production liife (20 yearrs).

Figure 30 3 Shape coonfigurationns of the steeel catenaryy riser.

57

Table 6 Fatigue dam mage sensittivity (vary outside diam meter) Case no. n

OD (in)

ID (in)

t (in n)

Dama ge per yearr Fatigue Life L (yr)

Case 1

13.00

11.0 00

1.0 00

8.98E-03

111 1

Case 2

13.50

11.0 00

1.2 25

5.22E-03

191 1

Case 3

14.00

11.0 00

1.5 50

2.86E-03

349 9

Case 4

14.50

11.0 00

1.7 75

2.14E-03

467 7

Case 5

15.00

11.0 00

2.0 00

1.11E-03

899 9

F Figure 31 Mean von Miises combinned stress (v vary outsidee diameter).

58

Figure 332 Mean axiial stress proofile (vary outside o diam meter).

Figure 33 Mean bend ding stress profile p (vary y outside diameter).

59

Figure 34 3 Mean hooop stress proofile (vary outside o diam meter).

9.2. Sensitivit S ty Analyysis: Riseer Lengtth The purpoose of the sttudy is to finnd the optim mal ration of o the waterr depth and the halfspan of riiser (d/l) inn which it is able to minimize annual fatigue damagge at the touchdownn point. Ussing the sam me conditioon as the prrevious stud dy, 9 differrent riser lengths aree used. Thee length variies from 3,3300 to 3,7000 meters in 50 meter inncrement step. 6 the 1.32 half-span ratio r offers a minimum m annual From the below resuult in case 6, w is connsiderably longer l than n the expectted field fatigue daamage of 6002 years which productionn period (200 years). However, H thee model is based on thhe general sea s state conditionss; whereas the t random wave conditions with larger wavee height andd shorter return period in realitty can geneerate higherr stress resuulting in thee shorter fattigue life s will be scrutiniized furtherr in the of the risser. The issue of ranndom sea states probabilistic fatigue calculationns. All in all, this sttudy suggeests that thhe shape configurattion of the steel catenary (d/l) risser using 13” OD andd 11” ID shhould be around 1.3 32 in order to t maximize the fatigue life.

60

Figgure 35 Riseer shapes forr various length of riseer. Tabble 7 Cases for riser lenngth sensitivity analysiis Case no. n

Depth h/Half-Span

Length (m) (

Dama age per yea r Fatigue Life L (yr)

Case 1

0.56

3300

9 9.41E-03

106 6

Case 2

0.68

3350

2 2.96E-03

338 8

Case 3

0.81

3400

3 3.17E-03

315 5

Case 4

0.95

3450

3 3.48E-03

287 7

Case 5

1.10

3500

2 2.92E-03

342 2

Case 6

1.32

3550

1.66E-03

602 2

Case 7

1.56

3600

1.72E-03

582 2

Case 8

1.89

3650

2 2.59E-03

386 6

Case 9

2.27

3700

4 4.39E-03

228 8

61

Figure 36 Mean von Mises M stresss profiles (vvary length of riser).

3 Mean axxial stress prrofiles (varyy length of riser). r Figure 37

62

Figure 388 Mean ben nding stress profiles (vaary length of riser).

Figure 39 3 Mean ho oop stress prrofiles (vary y length of riser). r

63

9.3. Sensitivit S ty Analyysis: FPS SO Initiaal Positio on The purpose of the study s is to ensure thatt riser desiggn can survive from a extreme wave conndition. In the study, FPSO initiial positionns are shiftted from thhe mean position by b +10%, +5%, + -5% an nd -10% off the water depth. Theese horizonttal shifts are assum med as conseequences off the slow wave w drift motion m durinng the extrem me wave conditionss. In the exxtreme case,, wave heigght and wavve period are a assumedd at 8.59 meters annd 7.73 secoonds whichh are deriveed from thee extrapolattion of the Weibull extreme wave w correlaation. From the simulation, the results show that the t annual damage d incrreases whenn riser is stretched rather thann being slaccked. This iis because the initial position is situated where the tensile streess is dominnated over the t bendingg stress. Thee simulationn results w that the offfset distancce has signiificant effecct to the fatiigue damagge which also show can be observed o inn case 5. In I case 5, the FPSO O offset increases by 5% or approximaately 100 meters, m but itt significanttly decreasees the fatiguue life from 15 years to just 2 years. y Therrefore, it im mplies that the wave drift d effect may have a strong influence to the stresss and fatiguue of the riser. Howeveer, the studyy is simulateed in the extreme wave w conditiion where th he occurrennce probabillity is considderably low w.

w vary the t initial offfset of FPS SO. Figuure 40 Riser shape conffigurations when

64

Table 8 Faatigue damaage sensitivity analysiss (vary initiaal offset)

Case e no.

Offsett

Dam mage perr year

Fa atigue Liffe (yr)

Cas se 1

-10%

1.76E-01 1

6

Cas se 2

-5%

8.31E-02 2

12

Cas se 3

Mean

6.54E-02 2

15

Cas se 4

+5%

1.67E-01 1

6

Cas se 5

+10%

5.99E-01 1

2

Figure 41 Mean von Mises M combbined stress (vary initiaal offset).

65

Figuree 42 Mean axial a stress profile p (varry initial offfset).

Figure 43 4 Mean beending stress profile (vaary initial offset).

66

Figuree 44 Mean hoop h stress profile (varry initial offfset).

9.4. Sensitivit S ty Analyysis: FPS SO Size Under thee extreme wave w conditiion, the FPS SO’ size is varied from m 100 to 3550 meter in step of 50 meter. These T different sizes aree simulatedd in this studdy to investiigate the improvem ment of FPS SO’s stabilitty and deterrmine the optimal o FPS SO size resuulting in the minim mum fatigue damage. i F FPSO size will enhan nce the stabbility of From the sensitivity analysis, increasing f especially e i heave in FPSO beccause the inncreased siize shifts thhe natural frequency direction far off thee typical wave w frequeencies. Theerefore the inertia eff ffect can i heaave motion due to the wave w excitaation. As well, w the greater size suppress induced results in the larger hydrodynaamic dampinng force which w can minimize m thhe heave w makees riser life much longger. Howev ver, the sizee will be phhysically motions which limited by y the top faccilities and the field reqquirement. On the otheer hand, thee smaller size FPSO O will be treemendouslyy suffered from f the greeat effect off wave cleaarly seen in case 1, 2 and 3. Thhe study sugggests that a suitable siize of FPSO O should rannge from 250 to 3550 meters. Therefore, T the FPSO size in thiss study is purposed p too be 250 meters wh hich is approoximately th he same size of the Moontara FPSO O.

67

Table 9 Fatigue damage d senssitivity (varry vessel lenngth) Cas se no.

V Vessel length (m) Da amage pe er year Fa atigue Life e (yr)

Ca ase 1

100

5.07E+0 00

0

Ca ase 2

150

3.41E+0 00

0

Ca ase 3

200

2.88E-0 01

3

Ca ase 4

250

9.12E-0 03

110

Ca ase 5

300

3.11E-0 03

322

Ca ase 6

350

7.30E-0 04

1369

SO heave motion m (vary FPSO size)). Figgure 45 FPS

68

Figure 466 Mean von Mises com mbined stresss (vary FPSO size).

Figurre 47 Mean axial stresss profile (vaary FPSO sizze).

69

Figure 48 Mean bending stresss profile (vvary FPSO size). s

Figurre 49 Mean hoop stresss profile (vaary FPSO sizze).

70

9.5. Sensitivity Analysis: Simulation Time The purpose of the study is to find the optimum time step to minimize the computational error. Under the same condition as in the previous study, the simulation times vary from 10, 20, 30, 40, 50 and 60 minutes. Next, the fatigue damage derived from different simulation time will be scaled up to 1 year damage for the comparison. From the results, there is no significant difference among different cases which maybe because the steady wave assumption used in the study. If the waves are modelled by using irregular wave model e.g. JONSWAP, the simulation time may have more influence on the result accuracy. The study in the next chapter will be based on the regular wave assumption; therefore 10 minute simulation time will be used for e time effectiveness without sacrificing accuracy. Table 10 Fatigue damage sensitivity (vary simulation time) Case no.

Sim.time (min) Damage per year % Diff from Case1

Case 1

10

5.07E+00

100.00

Case 2

20

5.06E+00

99.92

Case 3

30

5.07E+00

99.92

Case 4

40

5.06E+00

99.94

Case 5

50

5.07E+00

99.97

Case 6

60

5.07E+00

99.98

71

9.6. Sensitivity Analysis: Length of Segment Under the same condition, the length per segment is varied from 10, 8, 6, 4 to 2 meter to investigate the effect of them with the result accuracy. Generally, the smaller the length is the better the accuracy, but simulation will become very time consuming process for a very fine segment. From the result, the segment length has negligible effect on the result accuracy. The first case result, assumed to have the highest accuracy because the length is the shortest, is just slightly different from other cases. The 4th case seems to be the optimum point because it will balance between accuracy and time required for simulation because it gives 96.6% accuracy before the accuracy decreases to 92.4% in case the next case. Hence, the length of 8 meters will be used to model the riser in the probabilistic fatigue analysis. Table 11 Fatigue damage sensitivity (vary length per segment) Case no.

Riser length/Segment (m) Damage per year % Diff from Case1

Case 1

2

5.48E+00

100.0

Case 2

4

5.44E+00

99.3

Case 3

6

5.37E+00

97.9

Case 4

8

5.29E+00

96.6

Case 5

10

5.06E+00

92.4

72

10. Probabilistic Fatigue Life 10.1. Waves for Fatigue Calculation Data available for this study included 1 year of measured directional wave data (1995 – 1996) from Jabiru location presenting the ambient wave data, and 35 years of modeled tropical cyclone wave height, period and direction time series to represent the storm wave climate. From the deterministic fatigue analysis, it provides estimates of the number of single waves that might affect a marine facility in a nominated lifetime. Modeled ambient data are combined with model storm data with the limit that Hs values should not exceed the return period value corresponding to the exposure period. The probability of occurrence of waves for a range of wave height intervals is determined for each Hs using the Forristall (1978) distribution shown below. The distribution and table represent wave height and wave period of individual waves generated in 20 years return periods in octane directions. In the probabilistic fatigue analysis, data in scatter diagrams are compressed into a smaller number of bins which the bins represent waves in a particular directions. The integration is done by selecting the wave period and lumping all wave height associated with that particular period. The equivalent wave height (Hse) for each period (Tz) is calculated by using the weighted average of wave numbers with the H6s due to the fact that stress range is raised to the approximate power of three of the S-N curve, and relationship between the wave height and the wave load has a power of two approximately. By this mean, the compressed sea state bins can be calculated and shown in the following table. Deterministic wave height distribution modeled by Forristall (1978) 2.263*(

prob(H  Ho )  e

Ho

Hs

)2.126

............................................ (26)

73

Table 12 Omnidirectional wave scatter diagram prepared for 20 years period Location:  Montara Field (Measured Jabiru data) Project:  J2464 Client:  Coogee Resources Direction Convention:  FROM Longitude:  124.538048     La tude:  −12.673610     DepthHeight:  −85.000000 m Montara Omnidirectional Components:  Storm, Ambient (Deterministic) Occurrence Matrix of Individual Wave Height (m) vs Average Zero Crossing Period (secs) Average Zero Crossing Period (secs) 3 to 4

4 to 5

5 to 6

6 to 7

   Individual Wave Height  12

12

0

0

Total 0 104002528 14456622 4395998 1526985 591847 242613 101624 42783 18001 7611 3296 1505 742 396 224 131 77 45 26 14 8 4 2 1 0 0 0 0 0 125393080

74

Table 13 Directional wave statistics prepared for 20 years period Location:  Montara Field (Measured Jabiru data) Project:  J2464 Client:  Coogee Resources Direction Convention:  FROM Longitude:  124.538048     La tude:  −12.673610     DepthHeight:  −85.000000 m Montara Omnidirectional Components:  Storm, Ambient (Deterministic) Occurrence Matrix of Individual Wave Height (m) vs Average Zero Crossing Period (secs) 337.5 to 22.5 . 1037965 161689 54447 22539 10296 4612 1877 685 232 79 29 13 6 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1294481

22.5 to 67.5 . 5391401 1102829 250895 45841 9218 2895 1439 868 547 347 220 139 87 54 33 20 12 7 4 2 1 0 0 0 0 0 0 0 0 6806874

67.5 to 112.5 . 7196918 2614662 1017012 327917 96958 26970 7301 2196 898 507 333 225 151 100 64 41 25 15 9 5 3 1 0 0 0 0 0 0 0 11292323

Average Zero Crossing Period (secs) 112.5 157.5 202.5 to to to 157.5 202.5 247.5 . . . 6528604 4458223 46853688 1532569 592579 4066729 525147 135480 912868 189321 35999 300611 69767 12418 128508 24765 5338 60600 8379 2537 29141 2793 1224 13811 978 572 6328 387 253 2773 182 105 1160 100 41 468 62 15 185 40 5 74 26 1 30 17 0 13 11 0 6 7 0 2 4 0 1 2 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8883175 5244796 52377000

   Individual Wave Height (m) 0 0.00 − 0.50 0.50 − 1.00 1.00 − 1.50 1.50 − 2.00 2.00 − 2.50 2.50 − 3.00 3.00 − 3.50 3.50 − 4.00 4.00 − 4.50 4.50 − 5.00 5.00 − 5.50 5.50 − 6.00 6.00 − 6.50 6.50 − 7.00 7.00 − 7.50 7.50 − 8.00 8.00 − 8.50 8.50 − 9.00 9.00 − 9.50 9.50 − 10.00 10.00 − 10.50 10.50 − 11.00 11.00 − 11.50 11.50 − 12.00 12.00 − 12.50 12.50 − 13.00 13.00 − 13.50 13.50 − 14.00 14.00       . Total . signifies no occurrence  Data description          : ambient+cyclonic Record period             : 06:38:00 02/12/1995  TO  11:12:00 20/12/1996  + 30 storms Exposure period           : 20.000000 years Total count               : 125392976

247.5 to 292.5 . 30933388 4037205 1386132 560006 246439 110443 48344 20145 7917 2943 1049 368 133 52 22 10 5 2 1 0 0 0 0 0 0 0 0 0 0 37354608

292.5 to 337.5 . 1602229 348366 114016 44750 18241 6986 2602 1058 526 319 214 147 100 65 41 25 15 8 4 2 1 0 0 0 0 0 0 0 0 2139725

Total 0 104002424 14456632 4395999 1526987 591847 242613 101624 42783 18001 7611 3296 1505 742 396 224 131 77 45 26 14 8 4 2 1 0 0 0 0 0 125392984

75

In the stuudy, waves will appro oach the FP PSO from 4 octant dirrections. Thhe wave height, waave period and a occurreence probabbility of wavves are show wn in the foollowing tables. Enntirely, theree are 3,072 2 load casess generated for the stuudy. The sim mulation results will be extraccted and annalyzed lateer in next chapter c to determine d thhe mean fatigue life fe of riser.

Figure 50 5 Wave sccatter diagraams prepareed in 4 direcctions.

76

Table 14 Occurrence matrix of directional wave for fatigue analysis (315⁰, 45⁰) Direction (0⁰)

Occurrence Matrix of Equivalent Wave Height (m) vs Equivalent Zero Crossing Period (secs)

Bin

1

2

3

4

5

6

7

8

9

10

Tze

3.50

4.50

5.50

6.50

7.50

8.50

9.50

10.50

11.50

12.50

Hse

0.65

1.03

1.23

1.46

4.52

5.28

.

.

.

.

.

.

.

.

Prob

4.58E‐03 1.91E‐02 1.64E‐02 5.92E‐03 3.43E‐05 3.70E‐06

Table 15 Occurrence matrix of directional wave for fatigue analysis (45⁰, 135⁰) Direction (90⁰)

Occurrence Matrix of Equivalent Wave Height (m) vs Equivalent Zero Crossing Period (secs)

Bin

1

2

3

4

5

6

7

8

9

10

Tze

3.50

4.50

5.50

6.50

7.50

8.50

9.50

10.50

11.50

12.50

Hse

0.62

1.00

1.42

1.50

4.10

5.18

5.41

1.81

.

.

.

.

Prob

1.36E‐02 8.40E‐02 4.99E‐02 5.14E‐03 7.77E‐05 2.56E‐05 4.17E‐06 3.06E‐06

Table 16 Occurrence matrix of directional wave for fatigue analysis (135⁰, 225⁰) Direction (180⁰)

Occurrence Matrix of Equivalent Wave Height (m) vs Equivalent Zero Crossing Period (secs)

Bin

1

2

3

4

5

6

7

8

9

10

Tze

3.50

4.50

5.50

6.50

7.50

8.50

9.50

10.50

11.50

12.50

Hse

0.56

0.83

1.55

1.51

1.63

0.81

1.01

1.81

.

.

.

.

Prob

4.72E‐02 1.40E‐01 5.46E‐02 2.84E‐02 1.21E‐02 3.68E‐03 2.62E‐04 3.06E‐06

Table 17 Occurrence matrix of directional wave for fatigue analysis (225⁰, 315⁰) Occurrence Matrix of Equivalent Wave Height (m) vs Equivalent Zero Crossing Period (secs)

Direction (270⁰) Bin

1

2

3

4

5

6

7

8

9

10

Tze

3.50

4.50

5.50

6.50

7.50

8.50

9.50

10.50

11.50

12.50

Hse

0.52

0.90

1.53

1.60

1.73

0.79

0.96

0.95

.

.

.

.

Prob

5.62E‐02 2.11E‐01 1.35E‐01 7.48E‐02 2.71E‐02 8.59E‐03 2.52E‐03 1.36E‐04

77

10.2.. Cumu ulative Stress S Prrobability Distrib butions After a strress historyy has been generated for f a collecction of casses, the cum mulative distributioon curves arre plotted too indicate thhe mean valuue of maxim mum stress and also stress rangge. The curvves are presented in thhe figures below. b The results r indicate that P100 max ximum von Mises M stresss and P100 stress rangee are approxximate at 1229.3 and 52.3 MPa,, and the P550 of both arre 122.4 andd 21.5 MPaa respectivelly. In additiion, both curves hav ve smooth and relativvely continuues shape which w impliies that if cracking c occurs, it will w grow stteadily and continuously.

F Figure 51 Cumulative C n of maximuum stress. probability distribution

78

Figure 522 Cumulativve probabiliity distributiion of stresss range.

10.3.. Fatigu ue Life Probabil P lity Distrributions In this study, lifetimee operating conditions c aare applied to evaluate the fatigue life. All binations thaat can contrribute signifficantly to fatigue f are being b accouunted for load comb when estaablishing thhe long terrm distributtion of the stress. Thhe effects of o cyclic response to primaryy wave heeights andd frequencies variatio ons are coombined. o second order o wave force is ignnored in thee study beccause the However, the effect of s is asssumed to able a to provvide sufficiient restorinng forces too restrict mooring system the FPSO to drift awaay from meaan position.. The fatigu ue life probbability disttribution is prepared in i the figurre below. From F the figures, thhe value of P10, P50 and a P90 aree 30, 85 and d 147 yearss which refe fer to the 90%, 50% % and 10% confidencee. Follow the t API 2R RP recommended pracctice, the fatigue liffe should be at least 3 times (SF F =3.0) of its i service life. Thereffore, the safety facttor calculatted at mean n value is 4.25 4 which meet m the API A design practices p (with 20 years approoximate serrvice life). Hence, thee designed configurattions are y and practiically achiev ved API staandard of thhe riser desiggn. technically

79

Figure 53 Cumulative C e probabilityy distributioon of the fattigue life.

Figuure 54 Probaability distriibution of thhe fatigue liife.

80

11. Discussion Fatigue life is critically important for the riser design because the riser failure could cause major accidents which are extremely harmful for human and environment. Therefore, several methods are developed to estimate the fatigue life of riser. One of them is by using computer simulation which engineers constructed the riser model based on the law of physics and experimental data to predict the stress and fatigue damage. However, the procedures for estimation are still complicated, inconvenient and required sophisticated computer software. Also, with lacking of powerful computer in the past, it is nearly impossible to solve the system of hundred differential equations simultaneously. Another problem is that the simulation requires several inputs which most of them must be accurately measured at certain locations or carefully collected from the experiment in the laboratory. All these make the simulation expensive, time consuming and unproductive methodology for the marginal projects. Alternatively, the riser analysis can be done by deterministic calculations which the calculations are simplified by substituting input at the mean value to reduce the simulation tasks and complexity of the overall process. However, the results are highly uncertain, inclined to erroneous and unreliable especially for situations that environmental loads are distributed over a broad spectrum. In past several years, computer capability is incredibly improved. Now, a personal computer can manage million commands and solve thousands equations simultaneously which make the simulations is cheaper, simpler and easier and for engineer. The simulation has been extending to be more sophisticated and be able to include several interactions acted on the FPSO and riser. In this study, wave drift force and vortex induced vibration (VIV) may be very influential factors the riser fatigue life in certain circumstances such as deepwater productions. In the deepwater, riser design will become more critical because the service life of riser is very marginal when compared with the design fatigue life. Hence, these could be the potential research topic for the further investigation.

81

12. Conclusion In this study, a FPSO and riser models are constructed in Orcaflex which is the commercial software to analyze the riser properties. The environmental load included in the study is only the wave. Wind and current force are excluded from the study to simplify the models and they are believed that they have considerably less influence than the wave. In the Orcaflex, waves are simulated from the measured data in the Timor Sea where it would be a future deepwater project of PTTEP Australasia Limited. For the FPSO model, it is constructed based on the current FPSO used in Montana field. A primary engineering design for gas export riser has indicated that 13” OD with 1” thickness should be sufficient to withstand all stresses based on the API recommendations. Thereafter, sensitivity studies have been performed for several OD, riser length, FPSO offset and FPSO size to identify the values which the optimal fatigue life can be achieved. With the wall thickness of 1 inch, the study suggests that the riser’s depth over half-span should be about 1.32 to compromise between the tensile stress and the bending stress. And, this is where the minimal combined stress or so-called von Mises stress will be achieved. Next, the FPSO length overall (LOA) should be about 250 meters to achieve the good deck stability meanwhile not oversized the FPSO. Lastly, the probabilistic fatigue analysis reveals that the P50 fatigue life is 85 years. This number satisfies the safety standard used in the API 2RP. In summary, the study proves that the field development option by using FPSO and steel catenary riser (SCR) as production facility is a possible development scheme for the deepwater development in Timor Sea.

82

13. Recommendations During the productions, the riser internal and external conditions should be monitored to reveal whether design conditions have been exceeded. Monitoring and recording fluid composition, internal pressure, external pressure and temperature in the situations of storms and accidental loads also should be carried out. Regularly, the riser should be visually examined for external damage, pipe distortion, excessive curvature, marine growth, corrosion, changing conditions of buoyancy modules and subsea buoys to ensure all equipment are in good condition. Moreover, the defection of any equipment should be documented properly. Internal and external corrosion should be measured appropriately by either direct or indirect method. The direct method such as short test pipe or corrosion coupons should be installed in the riser where the test material can be retrieved after certain intervals. As well as, the indirect corrosion measurement should be applied to confirm the degradation of riser. This information is essential to predict remaining life of the riser accurately. So as to, the design philosophy should begin with the FEED which carefully integrals the regular maintenances and inspections into the critical components of the system. Furthermore, the regular inspection and preventive replacement should be available, scheduled and clearly described in details as part of normal operating practices.

83

Reference Capitio, R. (1995). Wave predictions based on scatter diagram data. Lisbon, Portugal: National Laboratory of Civil Engineering (LNEC). Chaudhury, G. (1999). Design,Testing, and Installation of Steel Catenary Risers. OTC. OTC. Hatton, S. A. (1998). Steel Catenary Risers for Deepwater Environments. OTC. Houston, Texas,: OTC. J. Xu, A. J. (2006). Wave Loading Fatigue Performance of Steel Catenary Risers (SCRs) in Ultradeepwater Applications. OTC. Houston, Texas,: OTC. Karunakara, D. (1999). Steel Catenary Riser Configurations for North Sea Field Developments. OTC. Houston, Texas: OTC. NAKHAEE, A. (2010). Study of the fatigue life of steel catenary risers in interaction with the seabed. Texas: Texas A&M University. O.B. Sertã, P. S. (1996). Steel Catenary Riser for the Marlim Field FPS P-XVIII . OTC. Houston, Texas: OTC. Quintin, H. (2007). Steel Catenary Riser Challenges and Solutions for Deepwater Applications . OTC. Houston, Texas: OTC. Resources, C. (2005). FINAL METOCEAN DESIGN CRITERIA, MONTARA FIELD. MetOcean Engineers Pty Ltd. Shi, C. (2008). Risk-based Fatigue Estimate of Deep Water Risers. Texas : University of Texas at Austin. Tapan K Sen, K. B. (2008). Fatigue in Deep Water Steel Catenary Risers–A Probabilistic Approach for Steel Catenary Riser. OTC. OTC 19425. Torres, A. L. (2008). Influence of Fatigue Issues on the Design of SCRs for Deepwater Offshore Brazil. OTC. Houston, Texas: OTC. Wirsching, P. (1984). Fatigue Reliability for Offshore Structures. ASCE J. Struct. Eng., Vol. 110, No. 10, Oct. 1984, 2340–2356.

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Appeendix I: I Plotts of D Displaccementt RAO Os

Fiigure 55 Displacement RAOs (Am mplitude, 0 degree d wave direction))

Figure 56 Displaceme D ent RAOs (P Phase, 0 deggree wave direction) d

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Figgure 57 Dissplacement RAOs R (Am mplitude, 30 degree wav ve direction)

Figure 58 Displacemen D nt RAOs (P Phase, 30 deegree wave direction) d

86

Figgure 59 Dissplacement RAOs R (Am mplitude, 60 degree wav ve direction)

Figure 60 Displacemen D nt RAOs (P Phase, 60 deegree wave direction) d

87

Figgure 61 Dissplacement RAOs R (Am mplitude, 90 degree wav ve direction)

Figure 62 Displacemen D nt RAOs (P Phase, 90 deegree wave direction) d

88

Figgure 63 Dispplacement RAOs R (Ampplitude, 120 0 degree wav ve directionn)

Figure F 64 Displacemen D nt RAOs (Phhase, 120 deegree wave direction)

89

Figgure 65 Dispplacement RAOs R (Ampplitude, 150 0 degree wav ve directionn)

Figure F 66 Displacemen D nt RAOs (Phhase, 150 deegree wave direction)

90

Figgure 67 Dispplacement RAOs R (Ampplitude, 180 0 degree wav ve directionn)

Figure F 68 Displacemen D nt RAOs (Phhase, 180 deegree wave direction)

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Appendix II: Tables of Displacement RAOs Table 18 Displacement RAOs (Relative angle = 0 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0.01 0.02 0.02 0.11 0.11 0.03 0.08 0.19 0.24 0.29 0.35 0.41 0.47 0.55 0.62 0.7 0.76 0.81 0.85 0.88 0.9 0.91 1

Phase (deg) 0 217 326 11 36 10 353 155 146 142 138 133 129 124 119 114 108 103 99 95 90 87.99 88 90

Sway Amplitude (m/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Displacement RAOs (Relative angle: 0 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (m/m) (deg) (m/m) (deg) 0 0 0 0 0 0 0.03 101 0 0 0 0.18 228 0 0 0 0.2 240 0 0 0 0.27 263 0 0 0 0.3 288 0 0 0 0.32 303 0 0 0 0.32 320 0 0 0 0.36 337 0 0 0 0.39 344 0 0 0 0.42 349 0 0 0 0.47 354 0 0 0 0.52 357 0 0 0 0.59 359 0 0 0 0.67 2 0 0 0 0.74 2 0 0 0 0.82 3 0 0 0 0.88 2 0 0 0 0.92 2 0 0 0 0.95 1 0 0 0 0.99 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0

Pitch Amplitude (m/m) 0 0.14 0.3 0.29 0.78 0.55 0.27 0.77 1.17 1.32 1.43 1.56 1.65 1.71 1.73 1.69 1.57 1.4 1.2 0.97 0.65 0.42 0.3 0

Phase (deg) 0 94 202 231 256 242 320 346 341 338 336 331 327 322 317 311 304 298 293 287 281 277 276 0

Yaw Amplitude (m/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Phase (deg) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Yaw Amplitude (m/m) 0 0.05 0.02 0.05 0.02 0.13 0.29 0.42 0.51 0.54 0.56 0.59 0.6 0.61 0.61 0.58 0.55 0.52 0.46 0.37 0.25 0.17 0.12 0

Phase (deg) 0 240 167 160 103 295 276 263 253 249 245 241 236 232 226 222 218 211 204 199 192 187 186 0

Table 19 Displacement RAOs (Relative angle = 30 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0 0.03 0.05 0.1 0.03 0.08 0.19 0.28 0.32 0.36 0.41 0.45 0.5 0.55 0.6 0.66 0.7 0.73 0.75 0.78 0.79 0.79 0.866

Phase (deg) 0 0 37 43 20 3 152 142 134 130 128 124 120 116 112 108 103 99 95 93 89 87 87 90

Sway Amplitude (m/m) 0 0.03 0.02 0.01 0.05 0.11 0.16 0.2 0.23 0.25 0.26 0.28 0.3 0.31 0.35 0.43 0.61 0.59 0.54 0.52 0.52 0.52 0.5 0.5

Displacement RAOs (Relative angle: 30 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (m/m) (deg) (m/m) (deg) 0 0 0 0 0 360 0.05 170 0.15 351 309 0.2 252 0.02 1 273 0.23 260 0.18 180 144 0.26 287 0.77 154 128 0.32 308 0.89 143 121 0.34 323 0.8 143 117 0.38 339 0.7 152 116 0.45 351 0.69 166 115 0.49 354 0.73 173 115 0.52 356 0.77 178 115 0.58 359 0.87 185 115 0.62 0 0.99 190 117 0.68 2 1.19 193 120 0.75 2 1.59 191 123 0.81 3 2.31 180 113 0.86 2 3.04 141 97 0.91 2 1.93 104 93 0.94 2 1.14 92 92 0.97 1 0.72 90 92 1 0 0.38 89 91 1 0 0.23 90 91 1 0 0.16 90 90 1 0 0 0

Pitch Amplitude (m/m) 0 0.11 0.37 0.5 0.65 0.3 0.78 1.22 1.5 1.58 1.64 1.7 1.72 1.72 1.68 1.59 1.43 1.25 1.07 0.85 0.56 0.37 0.26 0

Phase (deg) 0 142 256 265 255 303 344 339 333 330 326 322 319 316 310 305 299 294 289 286 280 277 275 0

92

Table 20 Displacement RAOs (Relative angle = 60 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0.01 0.02 0.03 0.14 0.23 0.3 0.34 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.47 0.48 0.48 0.5

Phase (deg) 0 347 145 152 140 126 115 108 104 101 100 98 96 94 92 90 88 86 84 84 83 83 84 90

Sway Amplitude (m/m) 0 0.02 0.12 0.15 0.26 0.35 0.42 0.48 0.52 0.54 0.56 0.58 0.6 0.62 0.66 0.75 0.92 0.97 0.93 0.9 0.9 0.9 0.87 0.866

Displacement RAOs (Relative angle: 60 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (m/m) (deg) (m/m) (deg) 0 0 0 0 0 247 0.09 259 0.18 131 95 0.22 331 0.89 120 96 0.26 339 0.89 120 100 0.39 352 0.81 135 102 0.5 2 0.86 155 103 0.63 6 1.01 166 103 0.73 6 1.14 174 104 0.79 5 1.27 177 104 0.82 5 1.34 179 104 0.84 5 1.41 180 104 0.86 4 1.51 183 105 0.88 3 1.64 185 107 0.9 3 1.84 187 109 0.93 2 2.22 184 112 0.95 2 2.89 175 108 0.96 1 3.57 147 98 0.98 1 2.72 116 93 0.99 1 1.78 102 92 0.99 1 1.22 97 91 1.01 0 0.65 93 91 1 0 0.39 92 90 1 0 0.28 92 90 1 0 0 0

Pitch Amplitude (m/m) 0 0.2 0.42 0.54 1.22 1.64 1.74 1.71 1.64 1.59 1.54 1.48 1.41 1.32 1.21 1.08 0.92 0.78 0.65 0.5 0.33 0.21 0.15 0

Phase (deg) 0 253 330 342 345 331 320 313 307 305 303 300 298 296 293 290 286 284 281 279 276 274 274 0

Yaw Amplitude (m/m) 0 0.05 0.12 0.2 0.5 0.7 0.8 0.85 0.86 0.86 0.85 0.83 0.81 0.78 0.73 0.67 0.59 0.54 0.47 0.38 0.26 0.17 0.12 0

Phase (deg) 0 129 249 253 246 237 229 223 219 217 215 212 210 208 205 203 202 199 195 191 187 184 183 0

Yaw Amplitude (m/m) 0 0.09 0.09 0.09 0.08 0.07 0.07 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.04 0.02 0.01 0 0 0 0

Phase (deg) 0 129 134 133 267 124 121 115 111 109 107 103 99 92 83 64 19 337 321 306 0 0 0 0

Table 21 Displacement RAOs (Relative angle = 90 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0 0.01 0.02 0.03 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0

Phase (deg) 0 0 60 60 43 27 19 18 19 20 21 23 25 27 28 31 34 37 39 42 47 54 63 0

Sway Amplitude (m/m) 0 0.27 0.4 0.42 0.5 0.56 0.6 0.63 0.65 0.66 0.67 0.68 0.68 0.68 0.69 0.72 0.94 1.08 1.07 1.04 1.04 1.04 1 1

Phase (deg) 0 10 49 53 66 73 78 81 83 85 86 88 89 91 95 103 109 99 94 91 90 90 90 90

Heave Amplitude (m/m) 0 0.16 0.45 0.52 0.83 1.03 1.08 1.07 1.08 1.07 1.06 1.05 1.05 1.04 1.03 1.03 1.02 1.02 1.01 1.01 1.01 1.01 1 1

Phase (deg) 0 15 42 42 36 24 14 9 6 5 4 3 2 2 1 1 0 0 0 0 0 0 0 0

Row Amplitude (m/m) 0 0.61 0.77 0.78 0.75 0.63 0.5 0.3 0.15 0.12 0.18 0.35 0.58 0.92 1.43 2.38 3.66 2.94 1.97 1.33 0.74 0.45 0.33 0

Phase (deg) 0 14 53 57 67 73 79 89 118 160 199 220 227 228 223 208 169 130 112 103 97 94 93 0

Pitch Amplitude (m/m) 0 0.08 0.18 0.2 0.22 0.17 0.11 0.08 0.06 0.04 0.04 0.03 0.03 0.02 0.01 0.01 0.01 0 0 0 0 0 0 0

Phase (deg) 0 318 309 302 266 234 213 198 190 186 183 179 175 170 165 157 142 0 0 0 0 0 0 0

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Table 22 Displacement RAOs (Relative angle = 120 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0.01 0.02 0.04 0.15 0.24 0.3 0.33 0.36 0.37 0.37 0.38 0.39 0.39 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.39 0.39 0.5

Phase (deg) 0 235 180 183 194 200 205 210 214 217 219 221 223 225 229 233 238 242 247 252 258 261 262 270

Sway Amplitude (m/m) 0 0.02 0.12 0.14 0.23 0.3 0.36 0.4 0.44 0.44 0.46 0.46 0.47 0.46 0.46 0.46 0.68 0.88 0.91 0.89 0.9 0.9 0.87 0.866

Displacement RAOs (Relative angle: 120 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (m/m) (deg) (m/m) (deg) 0 0 0 0 0 358 0.05 157 0.46 330 38 0.06 85 0.45 346 42 0.1 61 0.46 339 52 0.33 33 0.62 323 59 0.54 21 0.81 319 64 0.68 13 0.95 317 68 0.77 8 1.05 312 70 0.82 6 1.16 307 72 0.84 5 1.21 304 73 0.86 5 1.27 301 75 0.88 4 1.37 294 77 0.9 3 1.49 287 80 0.91 2 1.7 278 86 0.94 2 2.08 265 100 0.95 1 2.76 241 113 0.97 1 3.51 194 102 0.98 0 2.7 149 95 0.99 0 1.77 127 92 1 0 1.18 112 90 1.01 0 0.65 101 90 1 0 0.39 96 90 1 0 0.28 94 90 1 0 0 0

Pitch Amplitude (m/m) 0 0.18 0.49 0.69 1.42 1.76 1.83 1.78 1.69 1.64 1.59 1.51 1.44 1.35 1.23 1.1 0.94 0.79 0.65 0.51 0.33 0.21 0.15 0

Phase (deg) 0 197 30 39 52 56 58 60 63 64 65 66 67 69 71 73 75 77 80 82 84 86 86 0

Yaw Amplitude (m/m) 0 0.14 0.34 0.42 0.66 0.8 0.85 0.87 0.87 0.86 0.85 0.83 0.81 0.78 0.74 0.71 0.67 0.59 0.49 0.39 0.26 0.17 0.12 0

Phase (deg) 0 6 221 233 267 287 300 309 316 320 322 326 328 333 337 343 345 345 347 350 354 357 356 0

Yaw Amplitude (m/m) 0 0.06 0.15 0.14 0.01 0.19 0.35 0.47 0.54 0.57 0.59 0.61 0.62 0.62 0.61 0.6 0.6 0.54 0.46 0.37 0.25 0.17 0.12 0

Phase (deg) 0 37 331 346 15 241 260 274 285 289 294 299 303 308 316 324 331 333 338 343 349 353 355 0

Table 23 Displacement RAOs (Relative angle =150 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0.01 0.03 0.05 0.07 0.01 0.12 0.23 0.31 0.35 0.39 0.43 0.47 0.51 0.55 0.59 0.63 0.66 0.68 0.69 0.7 0.71 0.71 0.866

Phase (deg) 0 221 298 308 331 161 173 181 188 192 195 199 202 206 212 217 224 231 237 244 251 257 259 270

Sway Amplitude (m/m) 0 0.04 0.02 0 0.07 0.12 0.16 0.19 0.21 0.21 0.22 0.22 0.23 0.22 0.21 0.18 0.38 0.52 0.52 0.51 0.51 0.52 0.5 0.5

Displacement RAOs (Relative angle: 150 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (m/m) (deg) (m/m) (deg) 0 0 0 0 0 144 0.02 324 0.29 87 167 0.11 191 0.26 329 0 0.16 182 0.45 339 40 0.27 158 0.78 7 53 0.23 121 0.71 17 59 0.24 68 0.55 12 63 0.34 36 0.46 352 66 0.45 22 0.49 327 67 0.5 18 0.55 317 68 0.54 15 0.62 309 69 0.6 12 0.74 299 70 0.65 9 0.88 291 72 0.7 7 1.1 283 77 0.76 6 1.5 272 100 0.82 4 2.22 250 126 0.87 2 2.99 196 104 0.92 1 1.91 146 95 0.95 1 1.14 126 91 0.97 0 0.71 113 89 1 0 0.38 102 90 1 0 0.23 97 90 1 0 0.16 94 90 1 0 0 0

Pitch Amplitude (m/m) 0 0.15 0.49 0.61 0.43 0.35 0.98 1.4 1.64 1.71 1.76 1.8 1.81 1.79 1.74 1.63 1.46 1.27 1.07 0.85 0.56 0.37 0.26 0

Phase (deg) 0 316 184 192 218 6 27 35 40 42 45 48 49 52 57 60 65 68 72 76 80 83 85 0

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Table 24 Displacement RAOs (Relative angle = 180 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (m/m) 0 0.01 0.01 0.02 0.1 0.09 0.01 0.12 0.23 0.28 0.33 0.39 0.44 0.49 0.56 0.62 0.69 0.74 0.77 0.79 0.81 0.82 0.82 1

Phase (deg) 0 131 342 306 318 330 181 173 180 184 187 191 195 200 206 213 220 227 234 241 250 255 258 270

Sway Amplitude (m/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Displacement RAOs (Relative angle: 180 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (m/m) (deg) (m/m) (deg) 0 0 0 0 0 0 0.05 31 0 0 0 0.09 261 0 0 0 0.1 227 0 0 0 0.27 167 0 0 0 0.31 140 0 0 0 0.26 106 0 0 0 0.27 65 0 0 0 0.34 39 0 0 0 0.39 31 0 0 0 0.43 25 0 0 0 0.49 19 0 0 0 0.55 15 0 0 0 0.61 11 0 0 0 0.69 8 0 0 0 0.76 5 0 0 0 0.83 3 0 0 0 0.89 2 0 0 0 0.93 1 0 0 0 0.96 0 0 0 0 0.99 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0

Pitch Amplitude (m/m) 0 0.06 0.14 0.37 0.8 0.32 0.39 0.95 1.34 1.47 1.57 1.69 1.75 1.8 1.8 1.74 1.59 1.41 1.21 0.97 0.65 0.42 0.3 0

Phase (deg) 0 331 159 173 193 209 15 27 33 36 38 41 44 47 51 56 61 65 70 74 79 82 85 0

Yaw Amplitude (m/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Phase (deg) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Appeendix III: I Plots of Wavee Load d RAO Os

Figgure 69 Waave load RA AOs (Operatting draft, 0 degree wav ve directionn)

Figure 700 Wave loadd RAOs (Phhase, 0 degrree wave dirrection)

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Figgure 71 Wavve load RAO Os (Operatiing draft, 30 0 degree waave directionn)

Figure 72 Wave loadd RAOs (Phhase, 30 degrree wave diirection)

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Figgure 73 Wavve load RAO Os (Operatiing draft, 60 0 degree waave directionn)

Figure 74 Wave loadd RAOs (Phhase, 60 degrree wave diirection)

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Figgure 75 Wavve load RAO Os (Operatiing draft, 90 0 degree waave directionn)

Figure 76 Wave loadd RAOs (Phhase, 90 degrree wave diirection)

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Figuure 77 Wave load RAO Os (Operatinng draft, 120 0 degree waave directioon)

Figure 78 Wave load RAOs (Phaase, 120 deggree wave direction) d

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Figuure 79 Wave load RAO Os (Operatinng draft, 150 0 degree waave directioon)

Figure 80 Wave load RAOs (Phaase, 150 deggree wave direction) d

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Figuure 81 Wave load RAO Os (Operatinng draft, 180 0 degree waave directioon)

Figure 82 Wave load RAOs (Phaase, 180 deggree wave direction) d

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Appendix VI: Tables of Wave Load RAOs Table 25 Wave load RAOs (Relative angle = 0 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 277 366 354 1530 1270 288 692 1460 1740 2000 2230 2490 2590 2710 2640 2550 2270 1990 1610 1080 713 518 0

Phase (deg) 0 39 148 193 217 191 174 336 327 323 319 314 310 305 300 295 289 284 280 276 272 270 270 0

Sway Amplitude (kN/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Wave Load RAOs (Relative angle: 0 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 0 2560 288 0 0 0 9270 57 0 0 0 9750 69 0 0 0 9350 95 0 0 0 8150 123 0 0 0 6660 139 0 0 0 4820 159 0 0 0 4140 183 0 0 0 3970 194 0 0 0 3810 204 0 0 0 3630 217 0 0 0 3660 225 0 0 0 3450 240 0 0 0 3350 262 0 0 0 3600 290 0 0 0 4610 314 0 0 0 6250 329 0 0 0 7900 338 0 0 0 9840 344 0 0 0 12500 350 0 0 0 14100 353 0 0 0 14900 354 0 0 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 146000 182000 165000 323000 171000 59600 137000 163000 162000 154000 138000 128000 105000 91300 100000 120000 141000 146000 142000 115000 84400 65800 26000

Phase (deg) 0 282 32 62 90 77 165 194 193 194 196 198 200 212 233 259 273 280 282 282 284 288 293 0

Yaw Amplitude (kN/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Phase (deg) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Yaw Amplitude (kN/m) 0 31800 8410 20200 6410 35100 66700 83400 90800 91200 89800 87800 85100 78800 70600 58100 47300 36900 27100 16900 7560 3420 1790 0

Phase (deg) 0 64 352 345 289 122 103 91 81 77 74 70 65 62 56 53 50 44 38 35 32 31 34 0

Table 26 Wave load RAOs (Relative angle = 30 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 8 551 877 1380 340 803 1630 2140 2320 2480 2610 2730 2760 2710 2550 2400 2090 1800 1420 957 625 450 0

Phase (deg) 0 149 219 225 201 185 333 323 315 311 309 305 301 297 293 289 284 280 276 274 271 269 269 0

Sway Amplitude (kN/m) 0 1760 698 369 1830 2920 3360 3480 3490 3570 3500 3470 3520 3320 3400 3750 4740 3700 2730 2000 1290 844 595 0

Wave Load RAOs (Relative angle: 30 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 183 4330 357 6030 179 135 10300 81 1260 148 72 11100 89 2490 15 333 9110 119 9780 338 317 8700 141 10600 325 310 6850 159 9220 321 307 5620 180 7810 321 306 5310 199 7010 324 306 5180 206 6820 324 306 4940 212 6490 325 307 4710 221 6140 326 307 4540 227 6030 327 311 4080 241 5440 329 315 3750 260 5160 330 319 3860 290 4580 328 307 4730 312 4150 324 289 6370 329 3050 324 285 8000 339 2460 327 286 10000 344 1840 333 289 12600 349 1340 338 291 14100 353 960 344 294 14900 354 752 349 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 114000 225000 288000 269000 88500 184000 216000 207000 192000 174000 147000 130000 102000 85300 91400 107000 124000 129000 125000 99900 75300 58100 26000

Phase (deg) 0 329 87 96 88 141 186 185 184 185 184 188 191 205 227 255 269 277 279 283 285 290 296 0

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Table 27 Wave load RAOs (Relative angle = 60 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 272 378 540 1950 2690 2980 2910 2830 2750 2680 2550 2480 2320 2120 1870 1640 1370 1130 892 577 380 273 0

Phase (deg) 0 170 326 333 321 307 296 289 285 282 281 279 277 275 273 271 269 267 265 265 265 265 266 0

Sway Amplitude (kN/m) 0 973 4840 5640 7250 7990 8090 7910 7650 7520 7400 7090 6980 6570 6320 6350 6910 5980 4660 3450 2230 1460 1040 0

Wave Load RAOs (Relative angle: 60 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 57 7770 85 3900 334 284 11300 160 19100 297 284 12600 168 19700 297 288 13500 184 17900 303 291 13300 197 17000 310 292 13000 205 16000 313 293 11600 209 14700 314 294 10100 212 13800 315 295 9380 215 13300 315 295 8580 218 12800 315 295 7390 223 11900 314 297 6740 226 11500 315 299 5510 237 10500 316 302 4530 255 9530 315 306 4200 286 8320 314 302 4950 311 6880 310 291 6610 329 4940 313 286 8260 338 3900 317 286 10100 345 2850 328 288 12700 350 2140 335 291 14100 353 1620 342 293 14900 354 1250 348 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 208000 255000 311000 506000 516000 412000 299000 221000 187000 157000 120000 97700 67700 50000 53900 64200 75300 77600 73200 60900 46600 39200 26000

Phase (deg) 0 81 161 173 179 167 159 156 155 156 158 162 166 181 211 248 265 275 279 284 291 301 310 0

Yaw Amplitude (kN/m) 0 31800 50500 80700 160000 189000 184000 169000 153000 145000 136000 124000 115000 101000 84500 67100 50800 38400 27700 17400 7860 3420 1790 0

Phase (deg) 0 313 74 78 72 64 56 51 47 45 44 41 39 38 35 34 34 32 29 27 27 28 31 0

Yaw Amplitude (kN/m) 0 57200 37800 36300 25700 18900 16100 11900 10700 8440 8020 7440 7090 6460 5790 6010 5160 2840 1180 458 0 0 0 0

Phase (deg) 0 313 319 318 93 311 308 303 299 297 296 292 288 282 273 255 211 170 155 142 0 0 0 0

Table 28 Wave load RAOs (Relative angle = 90 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 5 182 348 416 465 395 255 228 216 205 190 181 165 147 169 145 119 98 76 61 40 29 0

Phase (deg) 0 325 243 242 224 208 200 199 200 201 202 204 206 208 209 212 215 218 220 223 229 236 245 0

Sway Amplitude (kN/m) 0 14900 14400 14500 13600 12700 11500 10300 9480 9090 8730 8170 7710 6950 6250 5680 6860 6590 5330 3980 2580 1690 1190 0

Wave Load RAOs (Relative angle: 90 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 194 14000 201 36300 197 234 23500 231 32200 237 238 25700 231 31900 241 251 29800 227 27500 255 259 28500 217 23600 263 264 22900 210 20100 269 268 17300 208 16900 274 270 13900 209 14900 277 272 12300 211 14000 280 273 10800 212 13300 282 276 8900 216 12200 285 277 7850 219 11300 287 280 6040 230 10100 290 286 4550 249 9140 295 297 4020 284 8060 298 304 4860 312 7120 301 292 6630 331 5300 303 287 8270 339 4230 310 285 10200 345 3090 319 287 12600 351 2300 331 290 14200 353 1780 340 293 14900 355 1410 349 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 81400 111000 118000 104000 75800 51900 40900 35700 32200 31400 29500 29200 27900 27000 26800 26400 26500 26300 26300 26300 26300 26000 26000

Phase (deg) 0 143 134 126 89 56 33 21 14 10 9 7 6 4 2 2 2 0 0 0 0 0 0 0

104

Table 29 Wave load RAOs (Relative angle = 120 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 262 378 712 2090 2800 2980 2820 2750 2680 2540 2420 2360 2150 1970 1700 1460 1200 985 759 491 309 222 0

Phase (deg) 0 57 3 5 15 21 26 31 35 38 40 42 44 46 50 54 59 63 68 73 80 83 84 0

Sway Amplitude (kN/m) 0 1630 4410 4840 6090 6590 6690 6350 6200 5840 5770 5280 5070 4410 3810 3240 4800 5320 4520 3400 2230 1460 1040 0

Wave Load RAOs (Relative angle: 120 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 172 4300 343 12700 156 218 3040 277 11300 197 222 4670 252 11100 198 233 11200 224 10700 206 240 14200 213 10300 214 246 13700 207 9700 223 250 11800 205 8540 232 253 9940 207 8050 239 255 9020 208 7400 243 256 8150 211 7270 247 259 6850 215 6530 253 261 6140 218 6170 258 265 4710 228 5540 266 273 3600 250 5290 276 294 3300 289 5130 286 311 4410 318 5180 291 297 6280 334 4030 290 289 8060 341 3200 297 286 10100 347 2310 313 287 12600 351 1840 329 290 14100 354 1500 339 293 14900 355 1210 347 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 188000 303000 403000 593000 559000 441000 324000 246000 214000 186000 152000 134000 111000 96400 93600 95100 97300 93900 86700 68900 51900 43100 26000

Phase (deg) 0 25 220 230 246 254 260 269 278 284 290 299 307 324 345 9 25 38 46 51 53 49 44 0

Yaw Amplitude (kN/m) 0 89000 143000 169000 212000 216000 196000 173000 155000 145000 136000 124000 115000 101000 85700 71100 57600 41900 28800 17900 7860 3420 1790 0

Phase (deg) 0 190 46 58 93 114 127 137 144 148 151 155 157 163 167 174 177 178 181 186 194 201 204 0

Yaw Amplitude (kN/m) 0 38200 63100 56500 3210 51300 80500 93400 96100 96200 94600 90800 87900 80100 70600 60100 51600 38400 27100 16900 7560 3420 1790 0

Phase (deg) 0 221 156 171 201 68 87 102 113 117 123 128 132 138 146 155 163 166 172 179 189 197 203 0

Table 30 Wave load RAOs (Relative angle = 150 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 275 546 872 963 124 1190 1970 2370 2540 2680 2740 2850 2810 2710 2510 2290 1970 1670 1310 859 562 404 0

Phase (deg) 0 39 121 130 152 344 354 2 9 13 16 20 23 27 33 38 45 52 58 65 73 79 81 0

Sway Amplitude (kN/m) 0 2340 461 392 2330 3010 3220 3170 3050 2850 2800 2550 2490 2080 1640 1030 2820 3200 2600 1950 1260 844 595 0

Wave Load RAOs (Relative angle: 150 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 320 1680 151 9110 287 358 5520 20 2910 144 168 7620 11 6290 163 219 9560 348 10200 201 234 6450 315 8930 220 242 4860 268 7070 229 246 4900 238 5590 235 249 5060 226 4610 238 250 4960 224 4080 238 251 4700 223 3830 240 252 4260 225 3300 241 253 4030 226 3090 244 255 3250 236 2600 247 260 2610 259 2290 256 299 2760 298 1980 271 327 3960 323 2020 292 299 5940 337 1850 293 289 7780 344 1560 299 285 9820 348 1210 311 286 12500 352 985 328 290 14100 354 842 340 293 14900 355 696 347 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 157000 301000 354000 180000 114000 234000 250000 232000 214000 197000 170000 155000 131000 119000 124000 134000 146000 146000 136000 108000 81200 62700 26000

Phase (deg) 0 144 15 23 54 199 227 241 253 259 267 278 286 305 332 359 20 34 44 52 57 58 55 0

105

Table 31 Wave load RAOs (Relative angle = 180 degree) Period (sec) 0 3.9 4.8 4.9 5.5 6 6.5 7 7.4 7.6 7.8 8.1 8.3 8.7 9.2 9.9 10.7 11.8 13 14.8 18.4 22.9 27 Infinity

Surge Amplitude (kN/m) 0 276 186 355 1380 1040 107 1030 1760 2030 2270 2480 2670 2700 2760 2640 2510 2210 1900 1500 994 649 467 0

Phase (deg) 0 312 163 129 140 151 4 354 1 5 8 12 16 21 27 34 41 48 55 62 72 77 80 0

Sway Amplitude (kN/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Wave Load RAOs (Relative angle: 180 degree) Heave Row Phase Amplitude Phase Amplitude Phase (deg) (kN/m) (deg) (kN/m) (deg) 0 0 0 0 0 0 4360 218 0 0 0 4710 90 0 0 0 4860 58 0 0 0 9330 357 0 0 0 8470 332 0 0 0 5560 304 0 0 0 4150 270 0 0 0 3860 247 0 0 0 3860 240 0 0 0 3690 236 0 0 0 3400 235 0 0 0 3320 235 0 0 0 2750 243 0 0 0 2340 264 0 0 0 2560 302 0 0 0 3820 326 0 0 0 5790 339 0 0 0 7640 344 0 0 0 9730 348 0 0 0 12400 352 0 0 0 14100 354 0 0 0 14900 355 0 0 0 17000 0 0 0

Pitch Amplitude (kN/m) 0 62300 87100 215000 333000 103000 93500 168000 187000 182000 173000 157000 147000 128000 120000 129000 144000 160000 162000 154000 124000 90700 70100 26000

Phase (deg) 0 158 348 4 27 50 211 232 245 252 259 270 281 300 326 356 17 32 43 51 58 59 58 0

Yaw Amplitude (kN/m) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Phase (deg) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

106

Appeendix V: Wa ave Scaatter Diagraams

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